The modified two sided approximations method and Pade approximants for solving the differential equation with variant retarded argument

摘要

The aim of this paper is to present an efficient numerical procedure for solving boundary value problems for a differential equation with retarded argument: x" (t) + a (t)x (t - tau (t)) = f (t), x(t) = phi(t) (lambda(0) less than or equal to t less than or equal to 0), x(T) = x(T), where 0 less than or equal to t less than or equal to T and a(t), f(t),tau(t) greater than or equal to 0 (0 less than or equal to t less than or equal to T) and phi(t) (lambda(o) less than or equal to t less than or equal to 0) are known continuous functions. A differential equation with retarded argument is computed by converting the obtained series solution into Pade (approximants) series. First we calculate power series of the given equation system then transform it into Pade (approximants) series form, which give an arbitrary order for solving differential equation numerically. (C) 2002 Elsevier Inc. All rights reserved. [References: 7]