The modified two sided approximations method and Padé 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−τ(t))=f(t),x(t)=ϕ(t)(λ0⩽t⩽0),x(T)=xT,where 0⩽t⩽T and a(t),f(t),τ(t)⩾0(0⩽t⩽T) and ϕ(t)(λ0⩽t⩽0) are known continuous functions. A differential equation with retarded argument is computed by converting the obtained series solution into Padé (approximants) series. First we calculate power series of the given equation system then transform it into Padé (approximants) series form, which give an arbitrary order for solving differential equation numerically.