How can I control an error caused by a singular jacobian in a function?

Dear all

My code is simple.

After deciding the values of c and d utilizing a 'for-loop', I would like to solve a first order boundary value problem using 'bvp4c', a built-in toll in MATLAB, within c ≤ x ≤ d. The goal is to check all the possible values of c and d and to discover the value of c and d to satisfy the first order boudary value problem.

My problem is that the for-loop does not continue because 'a singuar jacobian' is encountered when RD(c,d)is executed (I guess that bvp4c does not operate when the boundary conditions are not satisfied). How can I continue the for-loop until I find the values of c and d satisfying the boundary conditions?

The other is that I want to save all figures generated excuting a for-loop. But, I could not find any way to change the figure name at saveas(h, 'ODE','jpg'). This could be done if I add the number to the figure name.

If you give me any hint, I will be thankful to you.

    k = 0 ;
    m = 1 ;

    a = 0 ;
    b = 2*pi ;
    n = 5 ;

    del = (b-a)/n ;

    for i = a : del : b

            c = a + del*k ;

            k = k + 1 ;

            for j =  c : del : b

                d = c + del*m ;

                RD(c,d) ;

                m = m + 1 ; 

            end

        end 

     function sol = RD(m,n)

        solinit = bvpinit(linspace(m,n,15),0,-10) ;
        sol = bvp4c(@ode,@bcs,solinit) ;

        h = figure('visible','off') ;
        plot(sol.x, sol.y(1,:)) ; 
        saveas(h, 'ODE','jpg') ;

     function dydx = ode(x, y, A)

        s1 = 2*3^(1/2)*cos(y)^2 ;
        s2 = 3^(1/2)*cos(y)^2 ;
        s3 = -3^(1/2)*cos(y)^2 ;
        ds1dy =  4*3^(1/2)*sin(2*y)*cos(y)^2 ;
        dydx = -(3*cos(2*y) + sin(2*y)*cot(x))*s1 - s2 + s3 + A ;

     function res = bcs(ya, yb, A)

        res = [ ya + pi/4 ; yb - pi/4 ] ;