Journal of Applied and Computational Mechanics

A New Taylor Series based Numerical Method: Simple, Reliable, and Promising

Document Type : Research Paper

Authors

1 National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, China

2 School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China

3 School of Science, Xi'an University of Architecture and Technology, Xi'an, 710055, China

4 Department of Applied Sciences, NSIT, Bihta, Patna, 801106, India

5 Center for Data Science, Siksha ‘O’ Anusandhan University, ITER College, Bhubaneswar, 751030, India

6 Department of Mathematics, Indian Institute of Technology Patna, Patna, 801106, India

7 Department of Mathematics, Texas A&M University- Kingsville, 700 University Blvd, Kingsville, 78363-8202, Texas, USA

Abstract

Taylor series method is a simple analytical method, which is accessible to all non-mathematician, has slow convergence. This paper develops a new Taylor series based numerical method to overcome the shortcoming of the Taylor series while maintaining its simplicity. Some examples are given, showing its reliability and efficiency. The proposed method is also proved to be extremely effective for initial value problems and boundary value problems. The method provides a universal approach to various highly non-linear problems, and it sheds a bright light on numerical theories for practical engineering applications.

Keywords

Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 

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Journal of Applied and Computational Mechanics
Volume 9, Issue 4
October 2023
Pages 1122-1134