How to solve system of ODE's with Boundary Conditions using BVP4C? (I would be very helpful for you)

Can somebody explain me how to solve ODE's with boundary conditions using BVP4C? I've attached my ODEs with boundary conditions (and also graphs attached). Please assist me in coding this equation using BVP4C. Thank you ahead of time.

Note: M=0.0, 0.5, 1.0, 1.5 and 2.0

I would be very helpfull for your help.

Answer 1

[Torsten]

M = [0 0.5 1 1.5 2];
for i = 1:numel(M)
    bvpfcn = @(x,y)[y(2);y(3);-y(1)*y(3)+y(2)^2+M(i)*y(2);2*y(3)+2*y(1)*y(2)];
    bcfcn = @(ya,yb)[ya(1);ya(2)-1.0;ya(4);yb(2)];
    xmesh = linspace(0,5,50);
    solinit = bvpinit(xmesh,[0 0 0 0]);
    sol{i} = bvp4c(bvpfcn, bcfcn, solinit);
end
figure(1)
plot(sol{1}.x,sol{1}.y(1,:),sol{2}.x,sol{2}.y(1,:),sol{3}.x,sol{3}.y(1,:),sol{4}.x,sol{4}.y(1,:),sol{5}.x,sol{5}.y(1,:))

figure(2)
plot(sol{1}.x,sol{1}.y(2,:),sol{2}.x,sol{2}.y(2,:),sol{3}.x,sol{3}.y(2,:),sol{4}.x,sol{4}.y(2,:),sol{5}.x,sol{5}.y(2,:))

figure(3)
plot(sol{1}.x,sol{1}.y(3,:),sol{2}.x,sol{2}.y(3,:),sol{3}.x,sol{3}.y(3,:),sol{4}.x,sol{4}.y(3,:),sol{5}.x,sol{5}.y(3,:))

figure(4)
plot(sol{1}.x,sol{1}.y(4,:),sol{2}.x,sol{2}.y(4,:),sol{3}.x,sol{3}.y(4,:),sol{4}.x,sol{4}.y(4,:),sol{5}.x,sol{5}.y(4,:))

[Syed]

Thanks Indeed Sir

i never forget this help.

Answer 2

[Torsten]

Your remaining task: A loop over the values of M.

M = 1.0;
bvpfcn = @(x,y)[y(2);y(3);-y(1)*y(3)+y(2)^2+M*y(2);2*y(3)+2*y(1)*y(2)];
bcfcn = @(ya,yb)[ya(1);ya(2)-1.0;ya(4);yb(2)];
xmesh = linspace(0,5,50);
solinit = bvpinit(xmesh,[0 0 0 0]);
sol = bvp4c(bvpfcn, bcfcn, solinit);
plot(sol.x, sol.y(1:2,:), '-o')

[Syed]

@Torsten Thanks indeed sir

sir kindly remaining task: A loop over the values of M.

how to use loop in such problem.

[Torsten]

A free short course about MATLAB basics can help:

https://matlabacademy.mathworks.com/details/matlab-onramp/gettingstarted

[Syed]

@Torsten Thanks sir

Sir this coding is for 2 graphs (f(eta) and f'(eta)) and 3rd one is also plot in the same file i.e G(eta)

[Syed]

@Torsten Sir Kindly reply me

[Torsten]

The forum is no place where experienced MATLAB users do the tasks of users who have no experience with the software.

I already did most of the work by setting up your problem and applying "bvp4c" to it. Making a loop over the elements of M is a task that everybody who uses MATLAB should be able to do. If you have to continue using MATLAB, it's absolutely necessary for you to get the basics. That's why I suggested the online tutorial. If you don't want to get the basics, it's your decision, but in this case, it makes no sense starting to use the software at all.