Items tagged with bvp

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hello...i have a problem with this program.

I want to save the result(y,u(y)) in a text or another format file, but I encounter with this error message:

Error, (in fprintf) number expected for floating point formatBVP.mw
 

restart:

A1:= 5.5:  n:= 0.59:  A2:= 11818.:  h0:= 0.402e-3:
L:= .1:  dpx := -11823.9:  uc:= 0.44e-2:

ODE:= (A3,y)->
   (h0^(n+1)*L/sqrt(n)*(A1*exp(sqrt(n)*y/L)-A2*exp(-sqrt(n)*y/L))+dpx*y*h0^(n+1)+A3*(h0)^n)^(1/n)
;

proc (A3, y) options operator, arrow; (h0^(n+1)*L*(A1*exp(sqrt(n)*y/L)-A2*exp(-sqrt(n)*y/L))/sqrt(n)+dpx*y*h0^(n+1)+A3*h0^n)^(1/n) end proc

(1)

ODEINT:= proc(A3)
option remember;
local y;
   evalf(Int(ODE(A3,y), y= 0..1, epsilon= 1e-7)) - uc
end proc:

ReINT:= proc(A3x, A3y)
   Digits:= 15:
   Re(ODEINT(A3x + I*A3y))
end proc:

ImINT:= subs(Re= Im, eval(ReINT)):

Digits:= 7:
a3:= fsolve([ReINT, ImINT]);

[6.3610757968979, 0.]

(2)

A3:= Complex(a3[]);

6.3610757968979+0.*I

(3)

Solve as IVP:

Digits:= 15:
sol:= dsolve({diff(u(y),y) = ODE(A3,y), u(0)=0}, numeric, range=0..1,  output=listprocedure):

``

``

plots:-odeplot(
   sol, [[y, Re(u(y))], [y, Im(u(y))]], y= 0..1,
   legend= [real, imag], labels= [y, u(y)]
);

 

 

F53 := proc (y) options operator, arrow; U end proc; G53 := proc (y) options operator, arrow; Re(evalf[20](F53(y))) end proc; Temp3 := cat("u(y)-y.dat"); fd53 := fopen(Temp3, WRITE, TEXT); for i from 0 by 0.5e-1 to 1 do tt := i; u := eval(G53(y), y = tt); fprintf(fd53, "%10.5e %10.5e  \n", tt, u) end do; fclose(fd53)

Error, (in fprintf) number expected for floating point format

 

NULL


 

Download BVP.mw

 

please help me

thanks

 

the program shows that the error please verify it sirprogram11.mw

Hi, my dear friend,

i am solving 9 ODE with boundary conditionsNigam.mw

Eq1 := 2.*F1(eta)+diff(H1(eta), eta) = 0

2.*F1(eta)+diff(H1(eta), eta) = 0

(1)

Eq2 := F1(eta)^2-G1(eta)^2+(diff(F1(eta), eta))*H1(eta)-(diff(F1(eta), eta, eta)) = 0

F1(eta)^2-G1(eta)^2+(diff(F1(eta), eta))*H1(eta)-(diff(diff(F1(eta), eta), eta)) = 0

(2)

Eq3 := 2*F1(eta)*G1(eta)+H1(eta)*(diff(G1(eta), eta))-(diff(G1(eta), eta, eta)) = 0

2*F1(eta)*G1(eta)+H1(eta)*(diff(G1(eta), eta))-(diff(diff(G1(eta), eta), eta)) = 0

(3)

Eq4 := 4*F1(eta)*F3(eta)+H3(eta)*(diff(F1(eta), eta))+H1(eta)*(diff(F3(eta), eta))-2*G1(eta)*G3(eta)-2.*F1(eta)^2-1.5*H1(eta)-(diff(F3(eta), eta, eta)) = 0

4*F1(eta)*F3(eta)+H3(eta)*(diff(F1(eta), eta))+H1(eta)*(diff(F3(eta), eta))-2*G1(eta)*G3(eta)-2.*F1(eta)^2-1.5*H1(eta)-(diff(diff(F3(eta), eta), eta)) = 0

(4)

Eq5 := 2*F3(eta)*G1(eta)+4*F1(eta)*G3(eta)+H3(eta)*(diff(G1(eta), eta))-H1(eta)*(diff(G3(eta), eta))-2*F1(eta)*G1(eta)-1.5*H1(eta)*(diff(G1(eta), eta))-(diff(G3(eta), eta, eta)) = 0

2*F3(eta)*G1(eta)+4*F1(eta)*G3(eta)+H3(eta)*(diff(G1(eta), eta))-H1(eta)*(diff(G3(eta), eta))-2*F1(eta)*G1(eta)-1.5*H1(eta)*(diff(G1(eta), eta))-(diff(diff(G3(eta), eta), eta)) = 0

(5)

Eq6 := 4.*F3(eta)+diff(H3(eta), eta) = 0

4.*F3(eta)+diff(H3(eta), eta) = 0

(6)

Eq7 := 6*F1(eta)*F5(eta)-6*F1(eta)*F3(eta)+3.*F3(eta)^2+H1(eta)*(diff(F5(eta), eta))+H3(eta)*(diff(F3(eta), eta))+H5(eta)*(diff(F1(eta), eta))-1.5*(H1(eta)*(diff(F3(eta), eta))+H3(eta)*(diff(F1(eta), eta)))-G3(eta)^2-2*G1(eta)*G5(eta)-(diff(F5(eta), eta, eta)) = 0

6*F1(eta)*F5(eta)-6*F1(eta)*F3(eta)+3.*F3(eta)^2+H1(eta)*(diff(F5(eta), eta))+H3(eta)*(diff(F3(eta), eta))+H5(eta)*(diff(F1(eta), eta))-1.5*H1(eta)*(diff(F3(eta), eta))-1.5*H3(eta)*(diff(F1(eta), eta))-G3(eta)^2-2*G1(eta)*G5(eta)-(diff(diff(F5(eta), eta), eta)) = 0

(7)

Eq8 := 6*G5(eta)*F1(eta)+2*G1(eta)*F5(eta)+4*G3(eta)*F3(eta)-4*F1(eta)*G3(eta)-2*F3(eta)*G1(eta)+H1(eta)*(diff(G5(eta), eta))-1.5*(H1(eta)*(diff(G3(eta), eta))+H3(eta)*(diff(G1(eta), eta)))+H3(eta)*(diff(G3(eta), eta))+H5(eta)*(diff(G1(eta), eta))-(diff(G5(eta), eta, eta)) = 0

6*G5(eta)*F1(eta)+2*G1(eta)*F5(eta)+4*G3(eta)*F3(eta)-4*F1(eta)*G3(eta)-2*F3(eta)*G1(eta)+H1(eta)*(diff(G5(eta), eta))-1.5*H1(eta)*(diff(G3(eta), eta))-1.5*H3(eta)*(diff(G1(eta), eta))+H3(eta)*(diff(G3(eta), eta))+H5(eta)*(diff(G1(eta), eta))-(diff(diff(G5(eta), eta), eta)) = 0

(8)

Eq9 := 6.*F5(eta)+F3(eta)+diff(H5(eta), eta) = 0

6.*F5(eta)+F3(eta)+diff(H5(eta), eta) = 0

(9)

bcs1 := F1(0) = 0, F3(0) = 0, F5(0) = 0

F1(0) = 0, F3(0) = 0, F5(0) = 0

(10)

bcs2 := G1(0) = 1, G3(0) = 0, G5(0) = 0

G1(0) = 1, G3(0) = 0, G5(0) = 0

(11)

bcs3 := H1(0) = 0, H3(0) = 0, H5(0) = 0

H1(0) = 0, H3(0) = 0, H5(0) = 0

(12)

bcs4 := F1(10) = 0, F3(10) = 0, F5(10) = 0

F1(10) = 0, F3(10) = 0, F5(10) = 0

(13)

bcs5 := G1(10) = 0, G3(10) = 0, G5(10) = 0

G1(10) = 0, G3(10) = 0, G5(10) = 0

(14)

R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, Eq5, Eq6, Eq7, Eq8, Eq9, bcs1, bcs2, bcs3, bcs4, bcs5}), [F1(eta), F3(eta), F5(eta), G1(eta), G3(eta), G5(eta), H1(eta), H3(eta), H5(eta)], numeric, output = listprocedure)

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

 

``


Maple Worksheet - Error

Failed to load the worksheet 

Download Nigam.mwNigam.mw

then i got this error

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

i dont know where i need to change.. could you help me..

Hi Guyz 

I have a problem with a numerical solution.

with the boundary conditions mentioned in the file we want to solve the differential equation numerically and find omega by using the shooting method

numshooting.mw

i want to solve this equation,

y''(x)=5*exp(-10/y'(x)) on ]0,15[ with y(0)=0,y(15)=2 

can any one help me ? thank you

Respected member!

Please help me in finding the solution of this problem....
 

NULL

 

 

NULL

>   

``

NULL

restart

with(RealDomain):

r := .2:

k := 5;

5

(1)

BCSforNum1 := u(0) = 0, (D(u))(0) = 1+beta*(((D@@2)(u))(0)-(D(u))(0)*RealDomain:-`^`(k, -1)), (D(u))(m) = 0, ((D@@2)(u))(m) = 0;

u(0) = 0, (D(u))(0) = 1+.2*((D@@2)(u))(0)-0.4000000000e-1*(D(u))(0), (D(u))(6) = 0, ((D@@2)(u))(6) = 0

 

v(0) = 1, v(6) = 0

(2)

numsol1 := dsolve({BCSforNum1, BCSforNum2, ODEforNum1, ODEforNum2}, numeric, output = listprocedure)

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

 

``


 

Download mplprimes.mw

Dear please check once it showing an error program.mw as intial value is not conververging

Dear sir,

I tried to solve a fourth order problem. But I got the error message as better to use midpoint method. Can I know what is midpoint method and here I uploading the problem please verify it if I did anything mistake?program.mw


Please help me on this :

restart; with(PDETools), with(plots)

n := .3:

Eq1 := (1-n)*(diff(f(x, y), `$`(y, 3)))+(1+x*cot(x))*f(x, y)*(diff(f(x, y), `$`(y, 2)))-(diff(f(x, y), y))/Da+(diff(f(x, y), y))^2+n*We*(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), `$`(y, 3)))+sin(x)*(theta(x, y)+phi(x, y))/x = x*((diff(f(x, y), y))*(diff(f(x, y), y, x))+(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), x))):

Eq2 := (diff(theta(x, y), `$`(y, 2)))/Pr+Nt*(diff(theta(x, y), y))^2/Pr+Nb*(diff(phi(x, y), y))*(diff(theta(x, y), y))/Pr+(1+x*cot(x))*f(x, y)*(diff(theta(x, y), y)) = x*((diff(f(x, y), y))*(diff(theta(x, y), x))+(diff(theta(x, y), y))*(diff(f(x, y), x))):

Eq3 := Nb*(diff(phi(x, y), `$`(y, 2)))/(tau*Pr)+Nt*(diff(theta(x, y), `$`(y, 2)))/(tau*Pr)+(1+x*cot(x))*f(x, y)*(diff(phi(x, y), y)) = x*((diff(f(x, y), y))*(diff(phi(x, y), x))+(diff(phi(x, y), y))*(diff(f(x, y), x))):

ValWe := [0, 5, 10]:

bcs := {Nb*(D[2](phi))(x, 0)+Nt*(D[2](theta))(x, 0) = 0, f(0, y) = ((1/12)*y)^2*(6-8*((1/12)*y)+3*((1/12)*y)^2), f(x, 0) = 0, phi(0, y) = -.5*y, phi(x, 12) = 0, theta(0, y) = (1-(1/12)*y)^2, theta(x, 0) = 1, theta(x, 12) = 0, (D[2](f))(x, 0) = Da^(1/2)*(D[2, 2](f))(x, 0)+Da*(D[2, 2, 2](f))(x, 0), (D[2](f))(x, 12) = 0}:

pdsys := {Eq1, Eq2, Eq3}:

p1 := ans[1]:-plot(theta(x, y), x = 1, color = blue):

plots[display]({p1, p2, p3})

 

``


 

Download untitle_2_(1).mw

Respected member!
Please help me to find the solution of attached problem.

 


> subject to boundary conditions


``

 

 

NULL

restart

alpha := evalf(2*Pi*(1/180)); EP := .2; lambda := .1; HA := 5; RE := 20

ODEforNum := (1+EP)*(((D@@3)(F))(r)+4*alpha^2*(D(F))(r))+2*alpha*RE*F(r)*(D(F))(r)-HA*alpha^2*(D(F))(r)-3*EP*lambda*((1/2)*(D(F))(r)^2*((D@@3)(F))(r)+(D(F))(r)*((D@@2)(F))(r)^2)/alpha^2-EP*lambda*(72*F(r)^2*(D(F))(r)+2*(D(F))(r)^3+32*F(r)*(D(F))(r)*((D@@2)(F))(r)+2*F(r)^2*((D@@3)(F))(r)) = 0

1.2*((D@@3)(F))(r)-0.243693936e-3*(D(F))(r)+1.396263402*F(r)*(D(F))(r)-24.62104762*(D(F))(r)^2*((D@@3)(F))(r)-49.24209525*(D(F))(r)*((D@@2)(F))(r)^2-1.44*F(r)^2*(D(F))(r)-0.4e-1*(D(F))(r)^3-.64*F(r)*(D(F))(r)*((D@@2)(F))(r)-0.4e-1*F(r)^2*((D@@3)(F))(r) = 0

 
 

 

BCSforNum := F(0) = 1, (D(F))(0) = 0, F(1) = 0

Digits := 15

15

(2)

numsol := dsolve({BCSforNum, ODEforNum}, numeric, output = listprocedure)

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

 
 

 

 

 

 

 

 

 

Download MapleN.mw

hi.

how i can dsolve this differential equations?

thanks

ich.mw
 

restart; Digits := 50; dsol1 := dsolve({diff(F(eta), eta, eta, eta)+.5*H(eta)*((diff(F(eta), eta))^2+F(eta)*(diff(F(eta), eta, eta)))/G(eta)^2+2*(diff(G(eta), eta))*(diff(F(eta), eta, eta))/G(eta)-(diff(H(eta), eta))*(diff(F(eta), eta, eta))/H(eta) = 0, diff(G(eta), eta, eta)+H(eta)*((diff(F(eta), eta))*G(eta)+.5*F(eta)*(diff(eta, eta)))/G(eta)^2+2*(diff(G(eta), eta))^2/G(eta)-((diff(H(eta), eta))*(diff(H(eta), eta)))/H(eta)+(diff(F(eta), eta, eta))^2-(H(eta)/G(eta))^2 = 0, diff(H(eta), eta, eta)+(.5*1.3)*H(eta)*(5*(diff(F(eta), eta))*H(eta)+F(eta)*(diff(H(eta), eta)))/G(eta)^2+2*(diff(G(eta), eta))*(diff(H(eta), eta))/G(eta)-(diff(H(eta), eta))^2/H(eta)+(1.3*1.44)*H(eta)*(diff(F(eta), eta, eta))/G(eta)-(1.3*1.92)*(H(eta)/G(eta))^3 = 0, F(0) = 0, G(0) = 0, H(0) = 0, (D(F))(0) = 1, (D(F))(1) = 0, (D(G))(0) = 0, (D(H))(0) = 0}, 'maxmesh' = 900, numeric, output = listprocedure, method = bvp[middefer], abserr = 0.1e-2); fy := eval(F(eta), dsol1)

Error, invalid input: eval received dsol1, which is not valid for its 2nd argument, eqns

 

 

NULL


 

Download ich.mw

 

Respected member!
Please help me to find the solution of attached problem, I am a new user so pleaes forgive any mistakes.
 

``


``


``

NULL

NULL

restart

R := 2.0

2.0

(1)

ODEforNum := r^3*((D@@4)(F))(r)+r^2*R*((D@@3)(F))(r)*(F(r)-2/R)+R*((D(F))(r)-r*((D@@2)(F))(r))*(r*(D(F))(r)+3*(F(r)-1/R)) = 0:

numsol := dsolve({BCSforNum, ODEforNum}, numeric, output = listprocedure)

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

``


 

Download mplprimes.mw


 

refresh

refresh

(1)

G := 6.6743*10^(-8); 1; c := 2.99792458*10^10; 1; pi := 3.143; 1; rho := 5.3808*10^14

0.6674300000e-7

 

0.2997924580e11

 

3.143

 

0.5380800000e15

(2)

diff(P(r), r) = -G*(rho*c^2+P(r))*((4*pi*r^3*(1/3))*rho+4*Pi*r^3*P(r)/c^2)/(c^2*(r^2-2*G*r*(4*pi*r^3*(1/3))*rho/c^2)), diff(v(r), r) = 1.485232054*10^(-28)*((4*pi*r^3*(1/3))*rho+4.450600224*10^(-21)*Pi*r^3*P(r))/(r^2-1.485232054*10^(-28)*r*(4*pi*r^3*(1/3))*rho)

diff(P(r), r) = -0.7426160269e-28*(0.4836021866e36+P(r))*(0.2254913920e16*r^3+0.4450600224e-20*Pi*r^3*P(r))/(r^2-0.3349070432e-12*r^4), diff(v(r), r) = 0.1485232054e-27*(0.2254913920e16*r^3+0.4450600224e-20*Pi*r^3*P(r))/(r^2-0.3349070432e-12*r^4)

(3)

condition; -1; P(0) = 0, v(1014030) = -.4283

P(0) = 0, v(1014030) = -.4283

(4)

``


 

Download maple_soft.mw

I found the solution of P(r) at P(0)=0, but could obtain the result of v(r) at v(1014030)=-0.4283, v(r) may have a graph such that i can goes from -0.4283 to 0.

G := 6.6743*10^(-8);

a := 1.9501*10^24;

b := .3306;

c := 2.99792458*10^10;

d := 2.035;

pi := 3.143;

eps := 3.8220*10^35;

g(r) = 1-s(r)/0.06123;

j(r) = e^(-(1/2)*w(r))*(1-2*G*v(r)/(r*c^2))^.5

sys := diff(v(r), r) = 4*pi*r^2*eps/c^2, ics=v(0)=0

diff(u(r), r) = -G*(eps+u(r))*(v(r)+4*Pi*r^3*u(r)/c^2)/(c^2*(r^2-2*G*r*v(r)/c^2)),u(0)=1.3668*10^34

diff(w(r), r) = 1.485232054*10^(-28)*(v(r)+4.450600224*10^(-21)*pi*r^3*u(r))/(r^2-2*G*r*v(r)/c^2), conditions: w(0)=0,iterate it to find w(688240)=-2.05684, it solve must satistfy the both conditions.

diff(r^4*j(r)*(diff(g(r), r)), r)+4*r^3*g(r)*(diff(j(r), r)) = 0, conditions dg(r)/dr =0  at r=0, g(688240) =0.87214

diff(J(r), r) = (8*pi*(1/3))*(eps/c^2+u(r)/c^2)*(g(r)*j(r).(r^4))/(1-2*G*v(r)/(r*c^2)) condition J(0)=0.

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