Solve a boundary value problem of 2 differential equations and 3 boundary values.

I have a system of two coupled ode's. It is given that the left boundary values of both equations are the same at 493, wheras the right boundary value of the second equation is 293. The right value of the first equation is unknown. The goal is to calculate the right value of equation 1 and the profile of both equations. I can, however, not implement 1 of the 3 boundary values.

I have got the following equatons:

dT(1)=-((phi_h12(T(1),T(2)))/(phi_v*rho*Cp));

dT(2)=-((-phi_h12(T(1),T(2)) + phi_h2Inf(z,T(2)))/(phi_v*rho*Cp));

Where phi_v, rho and Cp are contants and phi_h12 and phi_h2Inf are equations to calculate these values. z, T(1) and T(2) are the values of the solver.

I tried to use the following code to approach this problem with bvp4c

x = linspace(0,1000);
y0 = [493 493];

bc=@(y0,y1)[y0(1)-493;y0(2)-493];
solinit = bvpinit(x,y0);

options = bvpset('RelTol',1e-6);
sol = bvp4c(@twoode,bc,solinit,options);

I just need to add the third boundary value.

Can you please help?

[Torsten]

You can't prescribe three boundary conditions for two equations - only two are allowed.

Maybe you have a free parameter in your equations that can be adjusted to fit the third condition ?

Best wishes

Torsten.

[Peter de Roode]

Thanks. It turned out that I had an error in one of the equations I used and that one of the values I thought were boundary condition was no boundary condition after all. Now it works.