High accuracy quintic spline solution of fourth order two-point boundary value problems

Abstract

It has been known for a long time that quintic spline collocation for fourth order two-point boundary value problems: y (4)+p(x)y=q(x), a<x<b, y(a)=α 0,y(b)=α 1, y′(a)=β 0, y′(b)=β 1, provides only 0(h 2) approximations; an order h 2 method using quintic splines was described by Usmani [8]. But quintic spline interpolation is an 0(h 6) process and therefore it is natural to look for an alternative method using quintic splines which would provide sixth order approximations. In the present paper we present a method using quintic splines which provides 0(h 6) uniformly convergent approximations for the solution of fourth order two-point boundary value problems.