We consider the numerical solution of two-point boundary value problem by collocation method using cubic spline. We derive asymptotic expansions of the errors which are a posteriori determined with little additional computation. The applications of these asymtotic expansions to a posteriori improvement of the approximate solution and adaptive mesh selection strategy (chopping procedure) are discussed. Some numerical results which closely correspond with the predicted theory are given.
Cite this article
Manabu Sakai, A Posteriori Improvement of Cubic Spline Approximate Solution of Two-Point Boundary Value Problem. Publ. Res. Inst. Math. Sci. 20 (1984), no. 1, pp. 137–149DOI 10.2977/PRIMS/1195181834