A New Methodology for the Development of Efficient Multistep Methods for First-Order IVPs with Oscillating Solutions-Reference-Cited by-同舟云学术

A New Methodology for the Development of Efficient Multistep Methods for First-Order IVPs with Oscillating Solutions

Published:2024-02-06 Issue:4 Volume:12 Page:504
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Simos Theodore¹²³⁴⁵⁶^ORCID

Affiliation:

1. School of Mechanical Engineering, Hangzhou Dianzi University, Er Hao Da Jie 1158, Xiasha, Hangzhou 310018, China

2. Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, West Mishref 32093, Kuwait

3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung City 40402, Taiwan

4. Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, Ulyanovsk 432027, Russia

5. Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Dongtong Road 705, Neijiang 641100, China

6. Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece

Abstract

In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory behind the development of the aforementioned approaches and show how it can be applied to the Adams–Bashforth approach in three steps. The stability of the new scheme is also analyzed. We compared the performance of our novel algorithm to that of established approaches and found it to be superior. Numerical experiments confirmed that, in comparison to standard approaches to the numerical solution of Initial Value Problems (IVPs), including oscillating solutions, our approach is significantly more effective.

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/4/504/pdf

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