Solving an Mixed Boundary Value Probelm?

Hi,

How do I solve a Mixed Boundary Value Problem with MatLab?

Thanks!

[Torsten]

What exactly is the problem ?

stationary/time-dependent ? 1d, 2d or 3d ? Which type of equation ?

Best wishes

Torsten.

[Avneet Singh]

One-dimensional problem of the following form:

y''(x) + f(x) y'(x) + g(x) y(x)=0 given y'(0) = a, y(1) = b

i.e. with variable coefficients. I was wondering if there is a function similar to ode45 or something to solve such problems?

Thanks,

A

[Torsten]

help bvp4c

Best wishes

Torsten.

Answer 1

[Ayush]

Hi @Avneet Singh

To solve a mixed boundary value problem (BVP) in MATLAB, as suggested by Torsten you can use the bvp4c or bvp5c functions as:

% Define the ODE system
function dydx = odefun(x, y, f, g)
    dydx = [y(2); -f(x)*y(2) - g(x)*y(1)];
end

% Define the boundary conditions
function res = bcfun(ya, yb, a, b)
    res = [ya(2) - a; yb(1) - b];
end

% Define f(x) and g(x) as inline functions or function handles
f = @(x) ...;
g = @(x) ...; 

% Initial guess for the solution
solinit = bvpinit(linspace(0, 1, 10), [0, 0]);

% Solve the BVP
sol = bvp4c(@(x, y) odefun(x, y, f, g), @(ya, yb) bcfun(ya, yb, a, b), solinit);

% Extract and plot the solution
x = linspace(0, 1, 100);
y = deval(sol, x);
plot(x, y(1, :));
xlabel('x');
ylabel('y(x)');
title('Solution of the Mixed Boundary Value Problem');

You can refer to the documentation of bvp4c for further details: https://www.mathworks.com/help/matlab/ref/bvp4c.html

I hope it helps!