Differential Transform Method for Some Delay Differential Equations

Baoqing Liu,Xiaojian Zhou,Qikui Du

doi:10.4236/am.2015.63053

Abstract

This paper concentrates on the differential transform method (DTM) to solve some delay differential equations (DDEs). Based on the method of steps for DDEs and using the computer algebra system Mathematica, we successfully apply DTM to find the analytic solution to some DDEs, including a neural delay differential equation. The results confirm the feasibility and efficiency of DTM.

Highlights

The differential transform method (DTM) is a semi analytical-numerical technique depending on Taylor series for solving integral-differential equations (IDEs)
Remark 3 If we want to improve the accuracy of the approximate solution in each interval, we can combine the above method with the multi-step method given by [17]
We apply DTM based on the method of steps to solve some delay differential equations, including neutral delay differential equations, successfully

Summary

Introduction

The differential transform method (DTM) is a semi analytical-numerical technique depending on Taylor series for solving integral-differential equations (IDEs). The method was first introduced by Pukhov [1] for solving linear and nonlinear initial value problems in physical processes. DTM has been used to obtain numerical and analytical solutions of ordinary differential equations [3], partial differential equations [4], eigenvalue problems [5], differential algebraic equations [6] [7], integral equations [8] and so on. Bereketoğlu [13] extend the method of differential transformation for solving the following two types of DDEs:. We will apply DTM to find the analytic solution to DDEs (3) with the help of the computer algebra system Mathematica. In some sense, our work can be viewed as a supplement to [13]

Differential Transform

Numerical Experiments

Findings

Conclusion