Spline collocation methods for solving delay-differential equations

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+cj) = x(i-1) + c(j)h, j = 1-3 be dependent on three parameters c(1), c(2), c(3) is an element of (0, 1) it will be shown that these methods for DDEs possess convergence rate of order seven if 0.7279115 less than or equal to c(1) < c(2) < c(3) < 1. Moreover, our methods are P-stable for 0.888035 less than or equal to 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. (C) 2002 Elsevier Inc. All rights reserved.