bvp4c Boundary Condition Issues

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Michael 2013-11-1

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Hi,

I'm trying to solve the following non linear ode with bvp4c:

y" + (P/(E*I))y = 0;

Where I is a known function of x, E is known constant, and P is an unknown constant. The following B.C.s exist:

y(0) = 0, y(L) = 0, y"(0) = 0

I want to use the following code to solve for P, but I get an error saying that the index ya(3) is out of bounds. Does bvp4c not work with second order boundary conditions? Does anyone know of any workarounds or other functions that could solve my problem?

    P = pi^2*mean(I)*E/L^2;
    dx = X(2) - X(1);
    solinit = bvpinit(X,@mat4init,P);
    sol = bvp4c(@mat4ode,@mat4bc,solinit);
    Sxint = deval(sol,X);
    Sxint = Sxint(1,:);
    plot(Sxint)
    disp(P)
    function dydx = mat4ode(x,y,P)
        Index = round(x/dx) + 1;
        dydx = [ y(2) 
                - P*y(1)/(E*I(Index)) ];
    end
    function res = mat4bc(ya,yb,P)
        res = [ ya(1)
                yb(1)
                ya(3) ];
    end
    function yinit = mat4init(x)
        yinit = [ sin(x*pi/L) 
                    pi/L*cos(x*pi/L) ];
    end