MATLAB: Non-linear coupled second order ODE with matlab

elasticitythin membrane

Dear All,
In attempt to compare an asymptotic solution to the exact solution of Reissner theory of elasticity, I will need to solve the following coupled equation :
D, A and q are constant and the boundary conditions are of clumped boundary conditions
I would be glad if there are hints to how to implement this in matlab.
Thanks a lot!

Best Answer

According to Torsten suggestions
function bvp4c_mathworks
rspan = [0.05 1];
init = zeros(1,4);
solinit = bvpinit(rspan,init);
sol = bvp4c(@ode4,@bc4,solinit);
r = sol.x;
Nr = sol.y(1,:);
b  = sol.y(2,:);
plot(r,Nr)
hold on
plot(r,b,'r')
hold off
legend('Nr(r)','\beta(r)')
end
function du = ode4(r,u)
Nr  = u(1);
b   = u(2);             % beta
dNr = u(3);             % d(Nr)/dr
db  = u(4);             % d(beta)/dr
cb = cos(b);            % cos(beta)
sb = sin(b);            % sin(beta)
A = 0.5;
D = 1.7;
q = 1;
du(1) = dNr;
du(2) = db;
du(3) = -(3*r*dNr + Nr + (1-cb)/A)/r^2;
du(4) = -(r*Nr*sb + r^2*q*cb)/D - db + sb/r;
du(4) = du(4)/r;
end
function res = bc4(u0, ur)
res = [ur(1)-0
       ur(2)-0
       ur(3)-0
       u0(2)-0];
end
Accept my answer please
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