Numerical Solution to second order coupled system of boundary value equations

Hello,

I have two second order coupled boundary value problems, and I could not find a method to solve them numerically

(d^2(s)/dx^2) = B(s-f);

(d^2(f)/dx^2) = (K(x)-B(s-f))/A;

Boundary Conditions:

s(0) = 0;

f(0) = 0;

at x=1; ds/dx = 0;

at x=1; df/dx = 0;

A and B are constants, and K(x) is known. I would like to find s(x), and f(x)

What is the most appropriate method and how can i solve the equations? Can you help on this?

[Davide Masiello]

I suggest an extensive reading of the relevant documentation

https://ch.mathworks.com/help/matlab/boundary-value-problems.html

[Sam Chak]

Hi @Oguz Altunkas

Since A, B, , and two of the initial values and are known, you can possibly use the SHOOTING METHOD with ode45 to solve the ODEs by considering the boundary conditions as a multivariate function of initial conditions at some point, reducing the boundary value problem to finding the initial values that satisfy .

Answer 1

[Torsten]

Use MATLAB's bvp4c.

[Oguz Altunkas]

bvp4c does not take K(x) as an input as far as i see

[Torsten]

Transfer the array K to the function where you define your ODEs.

Then, for a given value of x from bvp4c, you can use interp1 to interpolate the corresponding value of K(x) and insert this value into your function.