The modified successive approximations method and pade approximants for solving the differential equation with variant retarded argumend

摘要

In this paper, we propose a new approach for solving boundary value problems a differential equation with retarded argument: x"(t) + a(t)x(t - tau(t)) = f(t), x(t) = phi(t)(lambda0 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(0) 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 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) 2003 Elsevier Inc. All rights reserved. [References: 7]