How to solve nonlinear coupled ode by Shooting method .
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Chandan Kumawat
on 13 Oct 2019
Commented: darova
on 2 Nov 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 .
2 Comments
darova
on 13 Oct 2019
What have you tried? What ideas do you have? Did you see examples in MATLAB help?
Accepted Answer
More Answers (1)
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
10 Comments
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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