Spline collocation methods for solving delay-differential equations

Abstract

The convergence and stability analysis of seventh C 3-spline collocation methods if applied to delay-differential equations (DDEs), will be considered. Letting the interior collocation points x i−1+ c j = x i−1 + c j h, j=1–3 be dependent on three parameters c 1, c 2, c 3∈(0,1) it will be shown that these methods for DDEs possess convergence rate of order seven if 0.7279115⩽ c 1< c 2< c 3<1. Moreover, our methods are P-stable for 0.888035⩽ c 1< c 2< c 3<1. Numerical results illustrating the behavior of the methods when faced with some difficult problems are presented and the numerical results are compared to those obtained by other methods.