Asked by Chandan Kumawat
on 13 Oct 2019

Respected sir ,

I am getting problem to solve non linear coupled BVP by shooting method . Can you help me to solve that problem?

My problem is

F'''=(1/(1+epsilon1*(1-G)))*(A*F'+.5*t*A*F''+(F')^2-F*F''+epsilon1*G'*F''-lambda*G-delta*H+M*F'-(-1+epsilon1*G-epsilon1)*bita*F');

G''=(1/(1+epsilon2*G+Nr))*(Pr*(2*A*G+.5*A*t*G'+F'*G-F*G'-M*Ec*(F')^2-Ec*(1-epsilon1*G'+epsilon1)*(F'')^2)-epsilon2*(G')^2);

H''= Sc*(2*A*H+.5*A*t*H'+F'*H-F*H'+Rex*Zai*H);

where A=0 ; epsilon1= 0 ; epsilon2=1; lambda= 1; delta=1; bita=0; Nr=.1; Pr=5; M=.5;

Ec=.1 ; Sc=1; Rex= .3 ; Zai= .1 ;

and F(0)=0 , F'(0)=1 F'(infity)=0 G(0)=1 G(infity)=0 H(0)= 1 H(infity)=0

and F''(0) , G'(0) & H'(0) we have to guess

so tell me how to solve by shooting method with using rk -4 method .

Answer by Chandan Kumawat
on 14 Oct 2019

Accepted Answer

It is okey but my problem still remain same that how i do appropriate guess for according to your code

F2(0) & G1(0) & H1(0)

darova
on 1 Nov 2019 at 16:10

Why did you accept your answer instead of mine?

Chandan Kumawat
on 2 Nov 2019 at 7:26

here I'm not getting any option for accept your answer .

Thanks for solve my problem .

darova
on 2 Nov 2019 at 9:38

Whta is this?

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Answer by darova
on 14 Oct 2019

Try bvp4c

Suggestion:

F0 = y(1);

%% ...

H1 = y(7);

% and use these variables to make your code more redable

dy(1) = F1;

%% ..

You can also use temporary variables to make your code simpler

dy(3) = 1/(1+e1*(1-G0))* ...

(A*F1 + 0.5*t*A*F2 + F1^2 - F0*F2 + e1*G1*F2 - lambda*G0 - delta*H0 + M*F1 - (-1+e1*G0-e1)*bita*F1);

%%

TEMP0 = 1/(1+e1*(1-G0));

TEMP1 = 0.5*t*A*F2;

TEMP2 = e1*G1*F2;

TEMP3 = (-1+e1*G0-e1)*bita*F1;

dy(3) = TEMP0 * (A*F1 + TEMP1 + F1^2 - F0*F2 + TEMP2 - lambda*G0 - delta*H0 + M*F1 - TEMP3);

See attached scripts

darova
on 15 Oct 2019

constant value of M Ec Pr

Are you sure those values are correct? Maybe for something values diving by zero occurs?

Chandan Kumawat
on 17 Oct 2019

Thank you sir for give attention on my problem and now code is working well .

Can we solve it by ODE45 if yes then what values for F2(0) G1(0) & H1(0) should we take and how we will find that values .

darova
on 17 Oct 2019

I just changed main code

init = [0 1 -0.58 1 -1.52 1 -1.12];

% solinit = bvpinit([0 2],zeros(1,7));

% sol = bvp4c(@new,@bvpf,solinit);

[t,y] = ode45(@new,[0 2], init);

% plot(sol.x,sol.y)

plot(t,y)

legend('F','dF','d2F','G','dG','H','dH')

I took initial conditions from last calc. There is no rule for F2(0) G1(0) & H1(0) values, only guessing or something like bvp4c

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## 2 Comments

## darova (view profile)

## Direct link to this comment

https://fr.mathworks.com/matlabcentral/answers/485020-how-to-solve-nonlinear-coupled-ode-by-shooting-method#comment_755674

## Chandan Kumawat (view profile)

## Direct link to this comment

https://fr.mathworks.com/matlabcentral/answers/485020-how-to-solve-nonlinear-coupled-ode-by-shooting-method#comment_755956

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