A class of three-point spline collocation methods for solving delay differential equations

Abstract

In this paper a study of the existence, uniqueness, stability and convergence of a class of C 2-spline collocation methods for solving delay differential equations (DDEs) is introduced. Letting the interior collocation points , j=1(1)3 be dependent on the parameters c 1, c 2∈(0, 1) and c 3=1 it is shown that the proposed methods for DDEs possess a convergence rate of order six if 58−57(c 1+c 2)+55c 1 c 2=0, and they are unstable if c 1+c 2<1. Moreover, the methods are P-stable for 0.8028≤c 1<c 2. Numerical results illustrating the behaviour of the methods when faced with some difficult problems are presented and the numerical results are compared to those obtained by other methods.