Numerical Solution to second order coupled system of boundary value equations

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Oguz Altunkas
Oguz Altunkas 2022-4-4
评论： Torsten 2022-4-4
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?
  2 个评论
Sam Chak
Sam Chak 2022-4-4
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 .

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回答（1 个）

Torsten
Torsten 2022-4-4
Use MATLAB's bvp4c.
  2 个评论
Torsten
Torsten 2022-4-4
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.

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