JournalsprimsVol. 20 , No. 1DOI 10.2977/prims/1195181834

A Posteriori Improvement of Cubic Spline Approximate Solution of Two-Point Boundary Value Problem

  • Manabu Sakai

    Fukuoka University, Japan
A Posteriori Improvement of Cubic Spline Approximate Solution of Two-Point Boundary Value Problem cover

Abstract

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.