skiprun.m

function sol = skiprun
%SKIPRUN    Skipping rope BVP/eigenvalue example.

solinit = bvpinit(linspace(0,1,10),@skipinit,5);
sol = bvp4c(@skip,@skipbc,solinit);
plot(sol.x,sol.y(1,:),'-', sol.x,sol.yp(1,:),'--', 'LineWidth',3)
xlabel('x','FontSize',12)
legend('y_1','y_2')

% ------------------------ Local functions ------------------------
function yprime = skip(x,y,mu)
%SKIP    ODE/BVP skipping rope example.
%   yprime = SKIP(x,y,mu) evaluates derivative.
yprime = [y(2); -mu*y(1)];

function res = skipbc(ya,yb,mu)
%SKIPBC    ODE/BVP skipping rope boundary conditions.
%   res = skipbc(ya,yb,mu) evaluates residual.
res = [ya(1); ya(2)-1; yb(1)+yb(2)];

function yinit = skipinit(x)
%SKIPINIT    ODE/BVP skipping rope initial guess.
%   yinit = SKIPINIT(x) evaluates initial guess at X.
yinit = [sin(x); cos(x)];