MATLAB: Defining Boundary Conditions – How

boundary conditionsdifferential equationsMATLAB

Hello there,
I was trying to script the following ODE problem to solve it on matlab:
Considering the following bondary conditions:
What would be the best way to define the last two BCs?
How could I script then in MATLAB language?
Currently, I am using MATLAB R2015a.
Thank you for the help!
Gabriel

Best Answer

This link shows how to use bvp5c to solve multiple boundary condition problem: https://www.mathworks.com/help/matlab/math/solve-bvp-with-multiple-boundary-conditions.html. Try following code.
L = 3;
xmesh = [linspace(0, L/2, 50) linspace(L/2, L, 50)];
yguess = bvpinit(xmesh, [0; 0]);
sol = bvp5c(@odefun, @bcFun, yguess);
plot(sol.x, sol.y);
legend({'$y$', '$\dot{y}$'}, ...
    'Interpreter', 'latex', ...
    'FontSize', 16, ...
    'Location', 'best');
function dydx = odefun(x, y, region)
    W = 1;
    T = 2;
    dydx = zeros(2, 1);
    dydx(1) = y(2);
    
    if region==1
        dydx(2) = 3*W/T;
    else
        dydx(2) = W/T;
    end
end
function res = bcFun(yl, yr)
    res = [yl(1,1) - 0; % y(0)=0
           yr(1,1) - yl(1,2); % y(L/2-)=y(L/2+)
           yr(2,1) - yl(2,2); % y'(L/2-)=y'(L/2+)
           yr(1,2)]; % y(L)=0
end
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