The modified successive approximations method and padé 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−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 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.