Work

Ninth-Order Two-Step Methods with Varying Step Lengths

Year: 2025

Type: article

Abstract: This study investigates a widely recognized ninth-order numerical technique within the explicit two-step family of methods (a.k.a. hybrid Numerov-type methods). To boost its performance, we incorporate an economical step-size control algorithm that, after each iteration, either preserves the current step length, reduces it by half, or doubles it. Any additional off-grid points needed by this strategy are computed using a local interpolation routine. Indicative numerical experiments confirm the substantial efficiency gains realized by this method. It is particularly adept at resolving differential equations with oscillatory dynamics, delivering high precision with fewer function evaluations. Furthermore, a detailed Mathematica implementation is supplied, enhancing usability and fostering further research in the field. By simultaneously improving computational efficiency and accuracy, this work offers a significant contribution to the numerical analysis community.

Source: Mathematics

DOI: 10.3390/math13081257

Authors: Rubayyi T. Alqahtani, Theodore E. Simos, Charalampos Tsitouras

Institutions: Imam Mohammad ibn Saud Islamic University, Gulf University for Science & Technology, National and Kapodistrian University of Athens

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Al-Imam Muhammad Ibn Saud Islamic University