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Research Article | Open Access

Adams-Bashforth methods on bigeometric calculus

Mehmet Çağrı Yilmazer1, Sertac Goktas2, Emrah Yilmaz1( ), Mikail Et1
Department of Mathematics, Faculty of Science, Firat University, Elazığ, Türkiye
Department of Mathematics, Faculty of Science, Mersin University, Mersin, Türkiye
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Abstract

In this study, bigeometric Adams-Bashforth methods were defined as a strong alternative to classical numerical methods. After methods were established theoretically, error estimation formulas for each method were developed. Finally, a classical differential equation was converted to a bigeometric multiplicative differential equation, and it was solved by using bigeometric Adams-Bashforth methods. Then, error estimations were given.

Keywords

multiplicative calculusbigeometric Adams-Bashforth methodserror estimation
CLC number: 11A05, 65L05, 65L70

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AIMS Mathematics
Volume 10 Issue 8,
August 2025
Pages 18627-18640
DOI: 10.3934/math.2025832

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Cite this article:
Yilmazer MÇ, Goktas S, Yilmaz E, et al. Adams-Bashforth methods on bigeometric calculus. AIMS Mathematics, 2025, 10(8): 18627-18640. https://doi.org/10.3934/math.2025832

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Received: 15 January 2025
Revised: 01 July 2025
Accepted: 28 July 2025
Published: 15 August 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)