Eighth-Order Numerov-Type Methods Using Varying Step Length-Reference-Cited by-同舟云学术

Eighth-Order Numerov-Type Methods Using Varying Step Length

Published:2024-07-22 Issue:14 Volume:12 Page:2294
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Alshammari Obaid¹^ORCID,Aoun Sondess Ben²,Kchaou Mourad¹^ORCID,Simos Theodore E.³⁴⁵⁶^ORCID,Tsitouras Charalampos⁷^ORCID,Jerbi Houssem⁸^ORCID

Affiliation:

1. Department of Electrical Engineering, College of Engineering, University of Hail, Ha’il 81481, Saudi Arabia

2. Department of Computer Engineering, College of Computer Science and Engineering, University of Hail, Ha’il 81481, Saudi Arabia

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

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

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

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

7. General Department, National & Kapodistrian University of Athens, Euripus Campus, 34400 Psachna, Greece

8. Department of Industrial Engineering, College of Engineering, University of Hail, Ha’il 81481, Saudi Arabia

Abstract

This work explores a well-established eighth-algebraic-order numerical method belonging to the explicit Numerov-type family. To enhance its efficiency, we integrated a cost-effective algorithm for adjusting the step size. After each step, the algorithm either maintains the current step length, halves it, or doubles it. Any off-step points required by this technique are calculated using a local interpolation function. Numerical tests involving diverse problems demonstrate the significant efficiency improvements achieved through this approach. The method is particularly effective for solving differential equations with oscillatory behavior, showcasing its ability to maintain high accuracy with fewer function evaluations. This advancement is crucial for applications requiring precise solutions over long intervals, such as in physics and engineering. Additionally, the paper provides a comprehensive MATLAB-R2018a implementation, facilitating ease of use and further research in the field. By addressing both computational efficiency and accuracy, this study contributes a valuable tool for the numerical analysis community.

Funder

Research Deanship of Hail University-KSA

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/14/2294/pdf

Reference23 articles.

1. Unconditionally stable methods for second order differential equations;Hairer;Numer. Math.,1979

2. High order P-stable formulae for the numerical integration of periodic initial value problems;Cash;Numer. Math.,1981

3. Two-step fourth order P-stable methods for second order differential equations;Chawla;BIT,1981

4. Numerov Made Explicit has Better Stability;Chawla;BIT,1984

5. Explicit Numerov type methods with reduced number of stages;Tsitouras;Comput. Math. Appl.,2003