Hey everybody,
I have following problem. I have a system of coupled odes that I want to solve with a BVP solver. For the first ODE I have a Drichlet & Neumann boundary condition. For the second ode I have only a Drichlet boundary condition. Writting the code a stumbled across the problem, that there are too many boundary conditions. Is there a possibility that I can set three boundaries (mix between Drichlet and Neumann boundary) for a set of two ODE's?
Below the code:
% Define the range of the independent variable
xspan = [0, 1];
% Initial guess for the solution
solinit = bvpinit(linspace(0, 1, 5), @guess);
% Solve the BVP with bvp4c
sol = bvp4c(@odefun, @bc, solinit);
% Plot the results
xint = linspace(0, 1, 100);
yint = deval(sol, xint);
figure;
plot(xint, yint(1, :), '-o', xint, yint(2, :), '-x');
legend('y(x)', 'z(x)');
title('Solution of two separate first-order ODEs, one with Neumann BC');
xlabel('x');
ylabel('y, z');
function dydx = odefun(x, y)
a = y(1);
z = y(2);
dydx = [3*a-2*z; % da/dx = 3a - 2z
a^2]; % dz/dx = a^2
end
function res = bc(ya, yb)
% Boundary conditions
% a(0) = 1,
% a'(1) = 0,
% z(1) = 2,
res = [ya(1) - 1; % a(0) = 1, Dirichlet condition for a at x=0
yb(1); % a'(1) = 0, Neumann condition for a at x=1
yb(2) - 2]; % z(1) = 2, Dirichlet condition for z at x=1
end
function g = guess(x)
% Initial guesses for y and z
g = [0;
0];
end
