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iam trying to apply newton method on non liner system but i have a problem for apply while loop inside other while loop 
any help please

with(VectorCalculus):

NULL

f[1] := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(x^2, VectorCalculus:-`-`(VectorCalculus:-`*`(z, exp(y)))), VectorCalculus:-`-`(VectorCalculus:-`*`(y, exp(z)))), 61):

f[2] := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(x, y), z), VectorCalculus:-`-`(exp(x))), -3):

f[3] := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(x^2, y^2), z^2), -14):

F := Matrix([[f[1]], [f[2]], [f[3]]]):

FF := eval(F, [x = x[k], y = y[k], z = z[k]]):

X := Matrix([[x], [y], [z]]):

XX := eval(X, [x = x[k], y = y[k], z = z[k]]):

J := Jacobian([f[1], f[2], f[3]], [x, y, z]):

JJ := eval(J, [x = x[k], y = y[k], z = z[k]])

JJ := Matrix(3, 3, {(1, 1) = 2*x[k], (1, 2) = -z[k]*exp(y[k])-exp(z[k]), (1, 3) = -exp(y[k])-y[k]*exp(z[k]), (2, 1) = y[k]*z[k]-exp(x[k]), (2, 2) = x[k]*z[k], (2, 3) = x[k]*y[k], (3, 1) = 2*x[k], (3, 2) = 2*y[k], (3, 3) = 2*z[k]})

(1)

``

k := 0:

xi := convert(exp(-10), float):

maxval := 10^4:

NULL

while convert(Norm(FF, 2), float) > xi do alpha[k] := min(1, alpha[k]/lambda); L := 1/JJ.FF; K := -L*alpha[k]+XX; x[k+1] := evalf(Determinant(K[1])); y[k+1] := evalf(Determinant(K[2])); z[k+1] := evalf(Determinant(K[3])); A := convert(Norm(FFF, 2), float)^2; B := convert(Norm(FF, 2), float)^2; while A > B do L := 1/JJ.FF; alpha[k+1] := lambda*alpha[k]; K := -L*alpha[k+1]+XX; x[k+1] := evalf(Determinant(K[1])); y[k+1] := evalf(Determinant(K[2])); z[k+1] := evalf(Determinant(K[3])) end do; k := k+1 end do

alpha[0] := 1

 

L := Matrix(3, 1, {(1, 1) = -(12900-300*exp(8)-1200*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(2*exp(8)+31*exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(395/2)*(7*exp(8)-4*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500), (2, 1) = (84+exp(5))*(86-2*exp(8)-8*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(5/2)*(4+exp(8)+8*exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(79/4)*(exp(8)*exp(5)+8*exp(2)*exp(5)-16*exp(8)-128*exp(2)-400)/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500), (3, 1) = -(-39+4*exp(5))*(86-2*exp(8)-8*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(5/2)*(16+2*exp(8)+exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(79/4)*(2*exp(8)*exp(5)+exp(2)*exp(5)-32*exp(8)-16*exp(2)-100)/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)})

 

K := Matrix(3, 1, {(1, 1) = 5+(12900-300*exp(8)-1200*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(2*exp(8)+31*exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(395/2)*(7*exp(8)-4*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500), (2, 1) = 8-(84+exp(5))*(86-2*exp(8)-8*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(5/2)*(4+exp(8)+8*exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)-(79/4)*(exp(8)*exp(5)+8*exp(2)*exp(5)-16*exp(8)-128*exp(2)-400)/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500), (3, 1) = 2+(-39+4*exp(5))*(86-2*exp(8)-8*exp(2))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(5/2)*(16+2*exp(8)+exp(2))*(77-exp(5))/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)+(79/4)*(2*exp(8)*exp(5)+exp(2)*exp(5)-32*exp(8)-16*exp(2)-100)/(2*exp(8)*exp(5)+31*exp(2)*exp(5)-207*exp(8)-396*exp(2)-1500)})

 

14.35960152

 

-12.24471811

 

39.82986865

 

HFloat(5.911285325999999e36)

 

35235903.22

 

Warning,  computation interrupted

 

 

 

Hi, i wonder if there is a way to solve this 20×20 equations system for maple. Im trying fsolve but it doesn't work. aceitoso
 

nu := 6.1795*10^(-5)

0.6179500000e-4

(1)

varepsilon := 0.46e-1

0.46e-1

(2)

L__1 := 10.

10.

(3)

L__2 := 15.

15.

(4)

L__3 := 10.

10.

(5)

L__4 := 5*sqrt(2.)

7.071067810

(6)

L__5 := 6.

6.

(7)

L__6 := 6.

6.

(8)

L__7 := 20*sqrt(3.)*(1/3)

11.54700539

(9)

L__8 := 15.

15.

(10)

L__9 := 15.

15.

(11)

L__10 := 20.

20.

(12)

Re1 := 4*Q__1/(Pi*D__1*nu)

20604.24864*Q__1/D__1

(13)

Re2 := 4*Q__2/(Pi*D__2*nu)

20604.24864*Q__2/D__2

(14)

Re3 := 4*Q__3/(Pi*D__3*nu)

20604.24864*Q__3/D__3

(15)

Re4 := 4*Q__4/(Pi*D__4*nu)

20604.24864*Q__4/D__4

(16)

Re5 := 4*Q__5/(Pi*D__5*nu)

20604.24864*Q__5/D__5

(17)

Re6 := 4*Q__6/(Pi*D__6*nu)

20604.24864*Q__6/D__6

(18)

Re7 := 4*Q__7/(Pi*D__7*nu)

20604.24864*Q__7/D__7

(19)

Re8 := 4*Q__8/(Pi*D__8*nu)

20604.24864*Q__8/D__8

(20)

Re9 := 4*Q__9/(Pi*D__9*nu)

20604.24864*Q__9/D__9

(21)

Re10 := 4*Q__10/(Pi*D__10*nu)

20604.24864*Q__10/D__10

(22)

A__1 := (2.457*ln(1/((7/Re1)^.9+.27*varepsilon/D__1)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__1/Q__1)^.9+0.1242e-1/D__1))^16

(23)

A__2 := (2.457*ln(1/((7/Re2)^.9+.27*varepsilon/D__2)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__2/Q__2)^.9+0.1242e-1/D__2))^16

(24)

A__3 := (2.457*ln(1/((7/Re3)^.9+.27*varepsilon/D__3)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__3/Q__3)^.9+0.1242e-1/D__3))^16

(25)

A__4 := (2.457*ln(1/((7/Re4)^.9+.27*varepsilon/D__4)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__4/Q__4)^.9+0.1242e-1/D__4))^16

(26)

A__5 := (2.457*ln(1/((7/Re5)^.9+.27*varepsilon/D__5)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__5/Q__5)^.9+0.1242e-1/D__5))^16

(27)

A__6 := (2.457*ln(1/((7/Re6)^.9+.27*varepsilon/D__6)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__6/Q__6)^.9+0.1242e-1/D__6))^16

(28)

A__7 := (2.457*ln(1/((7/Re7)^.9+.27*varepsilon/D__7)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__7/Q__7)^.9+0.1242e-1/D__7))^16

(29)

A__8 := (2.457*ln(1/((7/Re8)^.9+.27*varepsilon/D__8)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__8/Q__8)^.9+0.1242e-1/D__8))^16

(30)

A__9 := (2.457*ln(1/((7/Re9)^.9+.27*varepsilon/D__9)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__9/Q__9)^.9+0.1242e-1/D__9))^16

(31)

A__10 := (2.457*ln(1/((7/Re10)^.9+.27*varepsilon/D__10)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__10/Q__10)^.9+0.1242e-1/D__10))^16

(32)

B__1 := (37530/Re1)^16

14680.75929*D__1^16/Q__1^16

(33)

B__2 := (37530/Re2)^16

14680.75929*D__2^16/Q__2^16

(34)

B__3 := (37530/Re3)^16

14680.75929*D__3^16/Q__3^16

(35)

B__4 := (37530/Re4)^16

14680.75929*D__4^16/Q__4^16

(36)

B__5 := (37530/Re5)^16

14680.75929*D__5^16/Q__5^16

(37)

B__6 := (37530/Re6)^16

14680.75929*D__6^16/Q__6^16

(38)

B__7 := (37530/Re7)^16

14680.75929*D__7^16/Q__7^16

(39)

B__8 := (37530/Re8)^16

14680.75929*D__8^16/Q__8^16

(40)

B__9 := (37530/Re9)^16

14680.75929*D__9^16/Q__9^16

(41)

B__10 := (37530/Re10)^16

14680.75929*D__10^16/Q__10^16

(42)

f__1 := 8*((8/Re1)^12+1/(A__1+B__1)^1.5)^(1/12)

8*(0.1173811769e-40*D__1^12/Q__1^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__1/Q__1)^.9+0.1242e-1/D__1))^16+14680.75929*D__1^16/Q__1^16)^1.5)^(1/12)

(43)

f__2 := 8*((8/Re2)^12+1/(A__2+B__2)^1.5)^(1/12)

8*(0.1173811769e-40*D__2^12/Q__2^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__2/Q__2)^.9+0.1242e-1/D__2))^16+14680.75929*D__2^16/Q__2^16)^1.5)^(1/12)

(44)

f__3 := 8*((8/Re3)^12+1/(A__3+B__3)^1.5)^(1/12)

8*(0.1173811769e-40*D__3^12/Q__3^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__3/Q__3)^.9+0.1242e-1/D__3))^16+14680.75929*D__3^16/Q__3^16)^1.5)^(1/12)

(45)

f__4 := 8*((8/Re4)^12+1/(A__4+B__4)^1.5)^(1/12)

8*(0.1173811769e-40*D__4^12/Q__4^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__4/Q__4)^.9+0.1242e-1/D__4))^16+14680.75929*D__4^16/Q__4^16)^1.5)^(1/12)

(46)

f__5 := 8*((8/Re5)^12+1/(A__5+B__5)^1.5)^(1/12)

8*(0.1173811769e-40*D__5^12/Q__5^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__5/Q__5)^.9+0.1242e-1/D__5))^16+14680.75929*D__5^16/Q__5^16)^1.5)^(1/12)

(47)

f__6 := 8*((8/Re6)^12+1/(A__6+B__6)^1.5)^(1/12)

8*(0.1173811769e-40*D__6^12/Q__6^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__6/Q__6)^.9+0.1242e-1/D__6))^16+14680.75929*D__6^16/Q__6^16)^1.5)^(1/12)

(48)

f__7 := 8*((8/Re7)^12+1/(A__7+B__7)^1.5)^(1/12)

8*(0.1173811769e-40*D__7^12/Q__7^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__7/Q__7)^.9+0.1242e-1/D__7))^16+14680.75929*D__7^16/Q__7^16)^1.5)^(1/12)

(49)

f__8 := 8*((8/Re8)^12+1/(A__8+B__8)^1.5)^(1/12)

8*(0.1173811769e-40*D__8^12/Q__8^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__8/Q__8)^.9+0.1242e-1/D__8))^16+14680.75929*D__8^16/Q__8^16)^1.5)^(1/12)

(50)

f__9 := 8*((8/Re9)^12+1/(A__9+B__9)^1.5)^(1/12)

8*(0.1173811769e-40*D__9^12/Q__9^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__9/Q__9)^.9+0.1242e-1/D__9))^16+14680.75929*D__9^16/Q__9^16)^1.5)^(1/12)

(51)

f__10 := 8*((8/Re10)^12+1/(A__10+B__10)^1.5)^(1/12)

8*(0.1173811769e-40*D__10^12/Q__10^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__10/Q__10)^.9+0.1242e-1/D__10))^16+14680.75929*D__10^16/Q__10^16)^1.5)^(1/12)

(52)

H__1 := piecewise(Q__1 > 0, 8000*10^6*f__1*L__1*Q__1^2/((9.8*(Pi^2))*D__1^5), -8000*10^6*f__1*L__1*Q__1^2/((9.8*(Pi^2))*D__1^5))

piecewise(0 < `#msub(mi("Q"),mi("1"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5)

(53)

H__2 := piecewise(Q__2 > 0, 8000*10^6*f__2*L__2*Q__2^2/((9.8*(Pi^2))*D__2^5), -8000*10^6*f__2*L__2*Q__2^2/((9.8*(Pi^2))*D__2^5))

piecewise(0 < `#msub(mi("Q"),mi("2"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^12/`#msub(mi("Q"),mi("2"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("2"))`/`#msub(mi("Q"),mi("2"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("2"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^16/`#msub(mi("Q"),mi("2"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("2"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("2"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^12/`#msub(mi("Q"),mi("2"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("2"))`/`#msub(mi("Q"),mi("2"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("2"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^16/`#msub(mi("Q"),mi("2"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("2"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("2"))`^5)

(54)

H__3 := piecewise(Q__3 > 0, 8000*10^6*f__3*L__3*Q__3^2/((9.8*(Pi^2))*D__3^5), -8000*10^6*f__3*L__3*Q__3^2/((9.8*(Pi^2))*D__3^5))

piecewise(0 < `#msub(mi("Q"),mi("3"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5)

(55)

H__4 := piecewise(Q__4 > 0, 8000*10^6*f__4*L__4*Q__4^2/((9.8*(Pi^2))*D__4^5), -8000*10^6*f__4*L__4*Q__4^2/((9.8*(Pi^2))*D__4^5))

piecewise(0 < `#msub(mi("Q"),mi("4"))`, 4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5, -4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5)

(56)

H__5 := piecewise(Q__5 > 0, 8000*10^6*f__5*L__5*Q__5^2/((9.8*(Pi^2))*D__5^5), -8000*10^6*f__5*L__5*Q__5^2/((9.8*(Pi^2))*D__5^5))

piecewise(0 < `#msub(mi("Q"),mi("5"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5)

(57)

H__6 := piecewise(Q__6 > 0, 8000*10^6*f__6*L__6*Q__6^2/((9.8*(Pi^2))*D__6^5), -8000*10^6*f__6*L__6*Q__6^2/((9.8*(Pi^2))*D__6^5))

piecewise(0 < `#msub(mi("Q"),mi("6"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5)

(58)

H__7 := piecewise(Q__7 > 0, 8000*10^6*f__7*L__7*Q__7^2/((9.8*(Pi^2))*D__7^5), -8000*10^6*f__7*L__7*Q__7^2/((9.8*(Pi^2))*D__7^5))

piecewise(0 < `#msub(mi("Q"),mi("7"))`, 7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5, -7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5)

(59)

H__8 := piecewise(Q__8 > 0, 8000*10^6*f__8*L__8*Q__8^2/((9.8*(Pi^2))*D__8^5), -8000*10^6*f__8*L__8*Q__8^2/((9.8*(Pi^2))*D__8^5))

piecewise(0 < `#msub(mi("Q"),mi("8"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5)

(60)

H__9 := piecewise(Q__9 > 0, 8000*10^6*f__9*L__9*Q__9^2/((9.8*(Pi^2))*D__9^5), -8000*10^6*f__9*L__9*Q__9^2/((9.8*(Pi^2))*D__9^5))

piecewise(0 < `#msub(mi("Q"),mi("9"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^12/`#msub(mi("Q"),mi("9"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("9"))`/`#msub(mi("Q"),mi("9"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("9"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^16/`#msub(mi("Q"),mi("9"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("9"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("9"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^12/`#msub(mi("Q"),mi("9"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("9"))`/`#msub(mi("Q"),mi("9"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("9"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^16/`#msub(mi("Q"),mi("9"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("9"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("9"))`^5)

(61)

H__10 := piecewise(Q__10 > 0, 8000*10^6*f__10*L__10*Q__10^2/((9.8*(Pi^2))*D__10^5), -8000*10^6*f__10*L__10*Q__10^2/((9.8*(Pi^2))*D__10^5))

piecewise(0 < `#msub(mi("Q"),mi("10"))`, 1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5, -1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5)

(62)

NULL

fsolve({Q__1 = Q__4, Q__3 = Q__7, 4*Q__1/(Pi*D__1^2) = 3.5, 4*Q__10/(Pi*D__10^2) = 3.5, 4*Q__2/(Pi*D__2^2) = 3.5, 4*Q__3/(Pi*D__3^2) = 3.5, 4*Q__4/(Pi*D__4^2) = 3.5, 4*Q__5/(Pi*D__5^2) = 3.5, 4*Q__6/(Pi*D__6^2) = 3.5, 4*Q__7/(Pi*D__7^2) = 3.5, 4*Q__8/(Pi*D__8^2) = 3.5, 4*Q__9/(Pi*D__9^2) = 3.5, H__1+H__4 = H__5+H__8, H__3+H__7 = H__6+H__10, Q__1+Q__5 = Q__2, Q__4+Q__8 = 980*(1/60), Q__5+Q__9 = Q__8+17, Q__7+Q__10 = 950*(1/60), Q__2+Q__3+Q__6 = 4000*(1/60), Q__9+Q__10+17.5 = Q__6}, {D__1 = 30, D__10 = 30, D__2 = 30, D__3 = 30, D__4 = 30, D__5 = 30, D__6 = 30, D__7 = 30, D__8 = 30, D__9 = 30, Q__1 = 20, Q__10 = 5, Q__2 = 40, Q__3 = 20, Q__4 = 20, Q__5 = 20, Q__6 = 20, Q__7 = 20, Q__8 = 5, Q__9 = 5})

fsolve({`#msub(mi("Q"),mi("1"))` = `#msub(mi("Q"),mi("4"))`, `#msub(mi("Q"),mi("3"))` = `#msub(mi("Q"),mi("7"))`, 4*`#msub(mi("Q"),mi("1"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("10"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("2"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("3"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("4"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("5"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("6"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("7"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("8"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("9"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^2) = 3.5, `#msub(mi("Q"),mi("1"))`+`#msub(mi("Q"),mi("5"))` = `#msub(mi("Q"),mi("2"))`, `#msub(mi("Q"),mi("4"))`+`#msub(mi("Q"),mi("8"))` = 49/3, `#msub(mi("Q"),mi("5"))`+`#msub(mi("Q"),mi("9"))` = `#msub(mi("Q"),mi("8"))`+17, `#msub(mi("Q"),mi("7"))`+`#msub(mi("Q"),mi("10"))` = 95/6, piecewise(0 < `#msub(mi("Q"),mi("1"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("4"))`, 4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5, -4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5) = piecewise(0 < `#msub(mi("Q"),mi("5"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("8"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5), piecewise(0 < `#msub(mi("Q"),mi("3"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("7"))`, 7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5, -7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5) = piecewise(0 < `#msub(mi("Q"),mi("6"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("10"))`, 1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5, -1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5), `#msub(mi("Q"),mi("2"))`+`#msub(mi("Q"),mi("3"))`+`#msub(mi("Q"),mi("6"))` = 200/3, `#msub(mi("Q"),mi("9"))`+`#msub(mi("Q"),mi("10"))`+17.5 = `#msub(mi("Q"),mi("6"))`}, {`#msub(mi("Q"),mi("1"))` = 20, `#msub(mi("Q"),mi("10"))` = 5, `#msub(mi("Q"),mi("2"))` = 40, `#msub(mi("Q"),mi("3"))` = 20, `#msub(mi("Q"),mi("4"))` = 20, `#msub(mi("Q"),mi("5"))` = 20, `#msub(mi("Q"),mi("6"))` = 20, `#msub(mi("Q"),mi("7"))` = 20, `#msub(mi("Q"),mi("8"))` = 5, `#msub(mi("Q"),mi("9"))` = 5, `#msub(mi("D",fontstyle = "normal"),mi("1"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("10"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("2"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("3"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("4"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("5"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("6"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("7"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("8"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("9"))` = 30})

(63)

NULL


 

Download aceitoso.mw

 

updated:
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
 
restart:
with(Groebner):
p1 := vector([a*cos(q1), a*sin(q1)]);
p2 := evalm(p1 + b*vector([cos(q1+q2), sin(q1+q2)]));
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
Pe := map(expand, P);
A := {cos(q1) = c1, sin(q1) =s1, cos(q2)=c2, sin(q2)=s2, cos(q3)=c3, sin(q3)=s3};
P := subs(A, op(Pe));
F1 := [x - P[1], y - P[2], s1^2+c1^2-1, s2^2+c2^2-1, s3^2+c3^2-1 ];
F2 := subs({a=1, b=1, c=1}, F1);
 
g2 := Basis(F2, plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[1], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[2], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[3], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[4], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[5], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[6], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[7], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[8], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[9], plex(c3, s3, c2, s2, c1, s1));
 
                                   1, c1
                               2       2    2   2
                           16 y  + 16 x , s1  s2
                                           2
                                 8 x, c1 s2
                                2      2    2  
                             2 y  + 2 x , s1  c2
                                 2 x, c1 c2
                            3            2        
                         2 x  - 2 x + 2 y  x, s2 c2
                                        2
                                   1, c2
                                   2 x, s3
                                    2, c3
originally i think
g2[1], g2[7], g2[9] have single variables c1, c2, c3 respectively
can be used to solve system
 
but without x and y, these equations can not be used
if choose leading term has x and y , but there is no single variable s1 or c1.
 
originally expect solve as follows
g2spec := subs({x=1, y=1/2}, [g2[3],g2[5],g2[6]]);
S1 := [solve([g2spec[1]])];
q1a := evalf(arccos(S1[1]));
q1b := evalf(arccos(S1[2]));
S2 := [solve(subs(s1=S1[1], g2spec[2])), solve(subs(s1=S1[2], g2spec[2])) ];
q2a := evalf(arccos(S2[1]));
q2b := evalf(arccos(S2[2]));
S3 := [solve(subs(s1=S2[1], g2spec[2])), solve(subs(s1=S2[2], g2spec[2])) ];
q2a := evalf(arccos(S3[1]));
q2b := evalf(arccos(S3[2]));
 

#first_question :how can i solve set of nonlinear ODEs,faster or using any packages ?
#second_question :what can be some boundary conditions for this type of nonlinear ODEs? how many BCs are required for this set of nonlinear ODEs? ( to use numeric solution)

 


 

restart:with(DEtools):with(DifferentialAlgebra):

eq[1]:=diff(N(r),r$2)+2/r*diff(N(r),r)+diff(phi(r),r)/phi(r)*diff(N(r),r)-mu^2/(32*phi(r))*N(r);

diff(diff(N(r), r), r)+2*(diff(N(r), r))/r+(diff(phi(r), r))*(diff(N(r), r))/phi(r)-(1/32)*mu^2*N(r)/phi(r)

(1)

eq[2]:=diff(phi(r),r$2)+2/r*diff(phi(r),r)-1/2*diff(phi(r),r)^2/phi(r)-8*diff(N(r),r)^2/(omega*(1-2*G*M/r))*phi(r);

diff(diff(phi(r), r), r)+2*(diff(phi(r), r))/r-(1/2)*(diff(phi(r), r))^2/phi(r)-8*(diff(N(r), r))^2*phi(r)/(omega*(1-2*G*M/r))

(2)

dsolve({eq[1],eq[2]});

``


 

Download nonlinear_ODE.mw

A system of algebraic equation

in terms of x, y, z

how draw 3 different circles to show the range of possible values for x, y and z respectively?

it may not be a circle 

It may be 3 bounded area graph to show the range of x , y , z respectively

 

updated

like the graph in many examples in

algebraic and geometric ideas in the theory of discrete optimization

bound area have color

Hi

I have a nonlinear PDEs, solved using finite difference in the square

I get the following nonlinear system of equation. Is there any idea how correct the code and display the solution.

I will appreciate any help in this question.

 

restart;
n:=100;
h:=1/(n+1);

# Boundary condition

for j from 0 by 1  to n+1 do
u[0, j] = 0;
u[n+1, j] = 0;
u[j, 0] = 0;
u[j, n+1] = 0 ;
end do;
## Loop for interior point in the square
for i from 1 by 1 to  n do
for j from 1 by 1 to  n do
(u[i+1, j]-u[i, j])*(u[i+1, j]-2*u[i, j]+u[i-1, j])+h*(u[i, j+1]-2*u[i, j]+u[i, j-1]) = 0;
end do;
end do;
 

How can I solve this system of equations with unknown u[i,j], where i,j=1,..,n

 

Many thanks for any help

Hi,

Can somebody help me to find out why Maple can't completely solve this system of differential equations?

The answer to the previous command is

but I don't get the solution for u(x). This should be u(x)=-x+x^2/2.

Thanks for your help

 

Hello guys,

I have some system of differential equations,

How can i find  eigenvalues of this system?

If i have solution

res := evalf(dsolve(sys union ics, convert(x, list), type = numeric, method = rkf45))

and

sol := evalf(dsolve(sys union ics, convert(x, list), method = laplace))

AnSolution.mw

Thanks!

I want to get solutions of this system ,can anyone help me ?solutions.mw

Hi, I am new in Maple. If I have an electric network as in the figure, I want to get the Transfer Function V2(s)/Vi(s) from this equation system:

Vi=R1.I1+V1

Vi=R2.I2+V2

I1-I2=C1.dV1/dt

I2=C2.dV2/dt

Which are the commands that I may write to get this?? Before hand, Thanks by your answers!

Dear 

Hope you will be fine. My file takes to much time to solve the system of nonlinear algebraic equations for Iterations=8. please solve my problem I will be waiting for positive response.

Error_graph.mw

$$\textbf{x}' = \begin{bmatrix} -4 & -2 \\ 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}+\begin{bmatrix} -t \\ -2t-1 \end{bmatrix},\textbf{x}(0)=\begin{bmatrix} 3 \\ -5 \end{bmatrix}$$

As I know firstly, when the matrix is denoted by $A$, we must compute $e^{At}$ by diagonalizing $A$: if $A=PDP^{-1}$ for a diagonal $D$ then $e^{At} = P e^{Dt} P^{-1}$ where $e^{Dt}$ is a diagonal matrix with $(e^{Dt})_{ii} = e^{D_{ii} t}$...
 
How can I write The Maple code? maple.stackexchange)

restart: with(LinearAlgebra):

A := Matrix(2,2,[-4,-2,3,1]);

....

Hello

Hope everything going fine with you. I am facing problem to fine the exact (numerical) solution of the attached system of linear PDEs associated with BSc and ICs. I tried to solve it without BCs and ICs, with BCs and with ICs also all the times I failed. Please solve it either general, with ICs or BCs. You can try to solve it numrically. In attached file H(t) represent the unit step function. I am waiting your positive response.

PDEs_solve.mw 

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

I meet a interesting nonlinear system in the analysis of an mechanics problem. This system can be shown as following:

wherein, the X and Y is the solutions. A, B, S, and T is the symbolic parameters.

I want to express X and Y with A, B, S, T. Who can give me a help, thanks a lot!

PS:the mw file is given here.

A_symbolic_nonlinear_system.mw

Dears;

Hope everyone is fine. I am try to find the numerical solutions of system of nonlinear algabric equation via newton's raphson method in the attached file but failed. Please see the attachment and try to correct. You can solve it least square method if possible. I am waiting your positive response. 

Help_in_Newton.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Email: muhammadusman@pku.edu.cn

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