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sharena2

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Default method??...

sharena2 50 Maple 18
ode dsolve numeric
September 02 2016
2 1

Hello all..

Im sharena and i am solving ODE BVP by using maple. i used this command to solved the equation..

 

However, i dont know which method this programm solved my ODE. Is it RK45 method??

Error, (in dsolve/numeric/bvp) unevaluat...

sharena2 50
ode differential-equation dsolve
April 10 2015
0 2

Dear Friends,

I am solving 6 ODEs using maple15. then i got this error. anyone know abou this? thank you.

problem2.mw

 

> 

 

> 

restart:with (plots): B:=1:M:=1:Gr:=0.5:Pr:=3:w:=0.02:blt:=5:Bi:=10:
> 

Eq1:=diff(f(eta),eta,eta,eta)-(diff(f(eta),eta))^(2)+f(eta)*diff(f(eta),eta,eta)+B*H(eta)*(F(eta)-diff(f(eta),eta))-M*diff(f(eta),eta)+Gr*theta(eta)=0;

diff(diff(diff(f(eta), eta), eta), eta)-(diff(f(eta), eta))^2+f(eta)*(diff(diff(f(eta), eta), eta))+H(eta)*(F(eta)-(diff(f(eta), eta)))-(diff(f(eta), eta))+.5*theta(eta) = 0

 (1)
> 

Eq2:=(1+Nr)*diff(theta(eta),eta,eta)+Pr*f(eta)*diff(theta(eta),eta)+(2/3)*H(eta)*B*(theta1(eta)-theta(eta))=0;

(1+Nr)*(diff(diff(theta(eta), eta), eta))+3*f(eta)*(diff(theta(eta), eta))+(2/3)*H(eta)*(theta1(eta)-theta(eta)) = 0

 (2)
> 

Eq3:=H(eta)*F(eta)+H(eta)*diff(G(eta),eta)+G(eta)*diff(H(eta),eta)=0;

H(eta)*F(eta)+H(eta)*(diff(G(eta), eta))+G(eta)*(diff(H(eta), eta)) = 0

 (3)
> 

Eq4:=F(eta)^2+G(eta)*diff(F(eta),eta)+B*(F(eta)-diff(f(eta),eta))=0;

F(eta)^2+G(eta)*(diff(F(eta), eta))+F(eta)-(diff(f(eta), eta)) = 0

 (4)
> 

Eq5:=G(eta)*diff(G(eta),eta)+B*(f(eta)+G(eta))=0;

G(eta)*(diff(G(eta), eta))+f(eta)+G(eta) = 0

 (5)
> 

Eq6:=G(eta)*diff(theta1(eta),eta)+l*B*(theta1(eta)-theta(eta))=0;

G(eta)*(diff(theta1(eta), eta))+l*(theta1(eta)-theta(eta)) = 0

 (6)
> 

bcs:=f(0)=0,(D(f))(0)=1,(D(theta))(0)=-Bi*(1-theta(0)),(D(f))(blt)=0,F(blt)=0,G(blt)=-f(blt),H(eta)=w,theta(blt)=0,theta1(blt)=0;

f(0) = 0, (D(f))(0) = 1, (D(theta))(0) = -10+10*theta(0), (D(f))(5) = 0, F(5) = 0, G(5) = -f(5), H(eta) = 0.2e-1, theta(5) = 0, theta1(5) = 0

 (7)
> 

L:=[0.5,1,1.5,2];

[.5, 1, 1.5, 2]

 (8)
> 

for k from 1 to 4 do p:=dsolve(eval({Eq1,Eq2,Eq3,Eq4,Eq5,Eq6,bcs},Nr=L[k]),[f(eta),F(eta),G(eta),H(eta),theta(eta),theta1(eta)],numeric,output=listprocedure);end do:

Error, (in dsolve/numeric/bvp) unevaluated names in system not allowed: {Y[9], Y[10]}

  
> 

``
> 

``

``

 

Download problem2.mw

Error, (in dsolve/numeric/bvp) initial N...

sharena2 50 Maple 12
ode differential-equation dsolve
January 12 2015
1 1

Dear All,

I am solving 6 ODE equations with boundary conditions using Runge kutta Felbergh 45 (Maple 12). then, i got this problem.. any suggestion??

Thank you :)

ISPC3.mw

``

> 

restart; with(plots); M := 3; k = .2; blt := 6; r := 2; l := .1; Pr := 6.8; Ec := 2; N := .5; rho := .5; Tv := .5; Tt := .5; c := 1; cm := .1; cp := .1
> 

Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0;

diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-3*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0

 (1)
> 

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0;

G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0

 (2)
> 

Eq3 := G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0;

G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0

 (3)
> 

Eq4 := G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0;

G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

 (4)
> 

Eq5 := diff(theta(eta), eta, eta)+Pr*(f(eta)*(diff(theta(eta), eta))-2*(diff(f(eta), eta))*theta(eta))+N*Pr*(theta1(eta)-theta(eta))/(rho*c*Tt)+N*Pr*Ec*(F(eta)-(diff(f(eta), eta)))^2/(rho*Tv) = 0;

diff(diff(theta(eta), eta), eta)+6.8*f(eta)*(diff(theta(eta), eta))-13.6*(diff(f(eta), eta))*theta(eta)+13.60000000*theta1(eta)-13.60000000*theta(eta)+27.20000000*(F(eta)-(diff(f(eta), eta)))^2 = 0

 (5)
> 

Eq6 := 2*F(eta)*theta1(eta)+G(eta)*(diff(theta1(eta), eta))+cp*(theta1(eta)-theta(eta))/(c*cm*Tt) = 0;

2*F(eta)*theta1(eta)+G(eta)*(diff(theta1(eta), eta))+2.000000000*theta1(eta)-2.000000000*theta(eta) = 0

 (6)
> 

bcs1 := f(0) = r, (D(f))(0) = -1, (D(f))(blt) = 0, F(blt) = 0, G(blt) = -f(blt), H(blt) = k, theta(0) = 1, theta(blt) = 0, theta1(blt) = 0;

f(0) = 2, (D(f))(0) = -1, (D(f))(6) = 0, F(6) = 0, G(6) = -f(6), H(6) = k, theta(0) = 1, theta(6) = 0, theta1(6) = 0

 (7)
> 

L := [0.1e-2];

[0.1e-2]

 (8)
> 

for k to 1 do R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, Eq5, Eq6, bcs1}, B = L[k]), [f(eta), F(eta), G(eta), H(eta), theta(eta), theta1(eta)], numeric, output = listprocedure); Y || k := rhs(R[2]); YP || k := rhs(R[3]); YR || k := rhs(R[4]); YQ || k := rhs(R[5]) end do

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

  
> 

R

R

 (9)
> 

print([(YP || (1 .. 1))(0)]);

[YP1(0)]

 (10)

``

> 

P1 := plot([YP || (1 .. 1)], 0 .. 14, labels = [eta, (D(f))(eta)]):

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

  
> 

plots:-display([P1]);

 
> 

``

``


Download ISPC3.mw

Error, (in dsolve/numeric/bvp/convertsys...

sharena2 50 Maple
ode differential-equation dsolve
January 01 2015
1 3

Dear All,

I am solving ODE with BC .. then im having this error.. (Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system)

Anyone could help me please?? :)

34.mw

``

> 

restart; with(plots); l := .1; M := .5; B := .6; c1 := 1; R := .5; Pr := .72; N := .5; rho := 1; Bt := .6; Ec := .5; lambda := .1; S := .5; blt := 5
> 

Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta))-2*(diff(f(eta), eta))^2+2*l*B*(diff(F(eta), eta)-(diff(f(eta), eta)))-M*(diff(f(eta), eta))-A*(2*(diff(f(eta), eta))+eta*(diff(f(eta), eta))) = 0;

diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(f(eta), eta))-2*(diff(f(eta), eta))^2+.12*(diff(F(eta), eta))-.62*(diff(f(eta), eta))-A*(2*(diff(f(eta), eta))+eta*(diff(f(eta), eta))) = 0

 (1)
> 

Eq2 := F(eta)*(diff(F(eta), eta))-2*(diff(F(eta), eta))^2+2*B*(diff(f(eta), eta)-(diff(F(eta), eta))-A*(eta*(diff(F(eta), eta))-2*(diff(F(eta), eta)))) = 0

F(eta)*(diff(F(eta), eta))-2*(diff(F(eta), eta))^2+1.2*(diff(f(eta), eta))-1.2*(diff(F(eta), eta))-1.2*A*(eta*(diff(F(eta), eta))-2*(diff(F(eta), eta))) = 0

 (2)
> 

Eq3 := (1+(4/3)*R)*(diff(theta(eta), eta, eta))+Pr*((diff(theta(eta), eta))*f(eta)-c1*(diff(f(eta), eta))*theta(eta))+2*N*Pr*Bt*(theta1(eta)-theta(eta))/rho+2*N*B*Pr*Ec*(diff(F(eta), eta)-(diff(f(eta), eta)))^2/rho-A*Pr*(4*theta(eta)+eta*(diff(theta(eta), eta)))+2*lambda*Pr*theta(eta)+Pr*Ec*(diff(f(eta), eta))^2 = 0;

1.666666667*(diff(diff(theta(eta), eta), eta))+.72*(diff(theta(eta), eta))*f(eta)-.72*(diff(f(eta), eta))*theta(eta)+.4320*theta1(eta)-.2880*theta(eta)+.21600*(diff(F(eta), eta)-(diff(f(eta), eta)))^2-.72*A*(4*theta(eta)+eta*(diff(theta(eta), eta)))+.360*(diff(f(eta), eta))^2 = 0

 (3)
> 

Eq4 := c1*(diff(F(eta), eta))*theta1(eta)-F(eta)*(diff(theta1(eta), eta))+2*gamma*Bt*(theta1(eta)-theta(eta))+A*(4*theta1(eta)+eta*(diff(theta1(eta), eta))) = 0;

(diff(F(eta), eta))*theta1(eta)-F(eta)*(diff(theta1(eta), eta))+1.2*gamma*(theta1(eta)-theta(eta))+A*(4*theta1(eta)+eta*(diff(theta1(eta), eta))) = 0

 (4)
> 

bcs1 := f(0) = S, (D(f))(0) = 1, (D(f))(blt) = 0, (D(F))(blt) = 0, F(blt) = f(blt)+blt*(D(f))(blt)-blt*(D(F))(blt), theta(0) = 1, theta(blt) = 0, theta1(blt) = 0;

f(0) = .5, (D(f))(0) = 1, (D(f))(5) = 0, (D(F))(5) = 0, F(5) = f(5)+5*(D(f))(5)-5*(D(F))(5), theta(0) = 1, theta(5) = 0, theta1(5) = 0

 (5)
> 

L := [.1, .15, .2];

[.1, .15, .2]

 (6)
> 

for k to 3 do R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, bcs1}, A = L[k]), [f(eta), F(eta), theta(eta), theta1(eta)], numeric, output = listprocedure); Y || k := rhs(R[3]); YP || k := rhs(R[4]); YR || k := rhs(R[5]); YQ || k := rhs(R[6]); YA || k := rhs(R[7]) end do

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

  
> 

``

``

 

Download 34.mw

Error, (in isolate) cannot isolate for a...

sharena2 50 Maple 12
ode numeric differential-equations
December 10 2014
3 12

Hello,

Im solving 4 ODE equations with BC. im trying to shoot the initial value but im having this error:

""Error, (in isolate) cannot isolate for a function when it appears with different arguments""

anyone could help me???

shooting92.mw

``

> 

restart
> 

Shootlib := "E:\\shooting/":
> 

libname := Shootlib, libname:
> 

with(Shoot):
> 

with(plots):
> 

n := 2:
> 

FNS := {F(eta), H(eta), f(eta), g(eta), u(eta), v(eta)}:
> 

ODE := {g(eta)*(diff(g(eta), eta))+B*(f(eta)+g(eta)) = 0, g(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-u(eta)) = 0, g(eta)*(diff(H(eta), eta))+H(eta)*(diff(g(eta), eta))+F(eta)*H(eta) = 0, diff(v(eta), eta)+f(eta)*v(eta)-u(eta)^2+B*H(eta)*(F(eta)-u(eta))-M*u(eta) = 0, diff(f(eta), eta) = u(eta), diff(u(eta), eta) = v(eta)};

{g(eta)*(diff(H(eta), eta))+H(eta)*(diff(g(eta), eta))+F(eta)*H(eta) = 0, g(eta)*(diff(g(eta), eta))+0.2e-1*f(eta)+0.2e-1*g(eta) = 0, g(eta)*(diff(F(eta), eta))+F(eta)^2+0.2e-1*F(eta)-0.2e-1*u(eta) = 0, diff(v(eta), eta)+f(eta)*v(eta)-u(eta)^2+0.2e-1*H(eta)*(F(eta)-u(eta))-3*u(eta) = 0, diff(f(eta), eta) = u(eta), diff(u(eta), eta) = v(eta)}

 (1)
> 

IC := {F(0) = gamma, H(0) = Q, f(0) = 0, g(0) = z, u(0) = 1, v(0) = alpha};

{F(0) = gamma, H(0) = Q, f(0) = 0, g(0) = z, u(0) = 1, v(0) = alpha}

 (2)
> 

BC := {F(L) = 0, H(L) = n, g(L) = -f(L), u(L) = 0};

{F(6) = 0, H(6) = 2, g(6) = -f(6), u(6) = 0}

 (3)
> 

infolevel[shoot] := 1:
> 

S := shoot(ODE, IC, BC, FNS, [alpha = 0, gamma = 0, z = -.2, Q = 0])

Error, (in isolate) cannot isolate for a function when it appears with different arguments

  
> 

``

``


Download shooting92.mw

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