Single-step and multi-step methods for Caputo fractional-order differential equations with arbitrary kernels

AIMS Mathematics

article

Parinya Sa Ngiamsunthorn¹  Danuruj Songsanga¹ 

[1] Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi;Center of Excellence in Theoretical and Computational Science ,(TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi

关键词: fractional differential equations;    numerical methods;    product integration;    single-step method;    multi-step method;   

DOI  :  10.3934/math.2022822

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

We develop four numerical schemes to solve fractional differential equations involving the Caputo fractional derivative with arbitrary kernels. Firstly, we derive the four numerical schemes, namely, explicit product integration rectangular rule (forward Euler method), implicit product integration rectangular rule (backward Euler method), implicit product integration trapezoidal rule and Adam-type predictor-corrector method. In addition, the error estimation and stability for all four presented schemes are analyzed. To demonstrate the accuracy and effectiveness of the proposed methods, numerical examples are considered for various linear and nonlinear fractional differential equations with different kernels. The results show that theses numerical schemes are feasible in application.

【 授权许可】

CC BY