Convergence Analysis of Implicit Euler Method for a Class of Nonlinear Impulsive Fractional Differential Equations

Yuexin Yu,Sheng Zhen,Luciano Mescia

doi:10.1155/2020/8826338

Abstract

For a class of nonlinear impulsive fractional differential equations, we first transform them into equivalent integral equations, and then the implicit Euler method is adapted for solving the problem. The convergence analysis of the method shows that the method is convergent of the first order. The numerical results verify the correctness of the theoretical results.

Highlights

In recent years, fractional differential equations have become a research hotspot due to their wide application in many fields
When the fractional differential equations are affected by instantaneous mutation, the impulsive fractional differential equations are obtained. e research of impulsive fractional differential equations can be found in literatures [10,11,12,13,14,15,16,17,18,19,20] and monograph
Implicit Euler method is constructed for solving a class of nonlinear impulsive fractional differential equations

Summary

Introduction

Fractional differential equations have become a research hotspot due to their wide application in many fields. We refer the readers to the research papers [1,2,3,4,5] and the monographs by Podlubny [6], Diethelm [7], Kilbas et al [8], Zhou [9], and the references cited therein. E research of impulsive fractional differential equations can be found in literatures [10,11,12,13,14,15,16,17,18,19,20] and monograph [21]. There are few literatures on numerical methods for impulsive fractional differential equations. Implicit Euler method is constructed for solving a class of nonlinear impulsive fractional differential equations. It is proved that the method is convergent of the first order. e numerical results verify the correctness of the theoretical results

Construction of Numerical Scheme

Convergence Analysis

Numerical Experiments

Conclusion