How to solve nonlinear coupled ode by Shooting method .

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Chandan Kumawat 2019-10-13

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https://ww2.mathworks.cn/matlabcentral/answers/485020-how-to-solve-nonlinear-coupled-ode-by-shooting-method

评论： darova 2019-11-2

采纳的回答： Chandan Kumawat

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 .

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darova 2019-10-13

What have you tried? What ideas do you have? Did you see examples in MATLAB help?

Chandan Kumawat 2019-10-14

I general do it with general shooting method but i'm getting problem how to do initial guess.

Here i'm attaching code which i have tried .

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Chandan Kumawat 2019-10-14

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https://ww2.mathworks.cn/matlabcentral/answers/485020-how-to-solve-nonlinear-coupled-ode-by-shooting-method#answer_396290

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)

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Chandan Kumawat 2019-11-2

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

Thanks for solve my problem .

darova 2019-11-2

Whta is this?

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darova 2019-10-14

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https://ww2.mathworks.cn/matlabcentral/answers/485020-how-to-solve-nonlinear-coupled-ode-by-shooting-method#answer_396232

在 MATLAB Online 中打开

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

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Chandan Kumawat 2019-10-17

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 2019-10-17

在 MATLAB Online 中打开

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')