Collocation spline methods in solving boundary value problems


Katarina Surla, Vladimir Jerković




The spline difference schemes for the problem: $-\varepsilon y''+p(x)y=f(x),y(0)=\alpha_0,y(1)=\alpha_1$, are considered. The error estimates have the optimal form $O(h^4/(\varepsilon+h^2))$. The different ways for derivation of the schemes and different possibilities for the global approximations are presented.