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Spline solution of some linear boundary value problems. (English) Zbl 1159.65077
The authors present a collocation method for the numerical solution of boundary value problems of high order for ordinary differential equations. The method is based on the use of high-order spline functions. In particular, the authors prove the convergence and stability of their scheme. Among the examples given in the paper, we find boundary value problems of orders 8, 10, and 12.
MSC:
65L10Boundary value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65L20Stability and convergence of numerical methods for ODE
34B05Linear boundary value problems for ODE