How to set Drichlet and Neumann boundary conditions for a set of ode in BVP solver

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

Answer 1

[Torsten]

Is there a possibility that I can set three boundaries (mix between Drichlet and Neumann boundary) for a set of two ODE's?

No. A first-order ODE (as the one for "a" in your code) needs a value for "a" either at the left or the right end of your interval of integration. Prescribing a derivative at either end is not possible with bvp4c (and mathematically wrong).