An adaptive semi-analytical approach in solving nonlinear korteweg-de vries equations

Abdul Rahman Farhan Sabdin and Che Haziqah Che Hussin and Jumat Sulaiman and Arif Mandangan and Essam Roshdy El-Zahar (2025) An adaptive semi-analytical approach in solving nonlinear korteweg-de vries equations. CFD Letters, 17. pp. 107-121. ISSN 2180-1363

Text FULL TEXT.pdf Restricted to Registered users only Download (583kB) | Request a copy

Abstract

This paper introduces a novel method named the Adaptive Hybrid Reduced Differential Transform Method (AHRDTM) for solving Nonlinear Korteweg-De Vries Equations (NKdVEs). AHRDTM provides convergent semi-analytical solutions over long-time frames by generating subintervals of varying lengths, significantly reducing the number of time-steps and processing time needed for solutions, distinguishing it from the traditional multistep approach of RDTM. Notably, AHRDTM avoids the need for perturbation, linearization or discretization, enhancing its adaptability and reliability. The findings demonstrate that AHRDTM provides highly accurate and efficient solutions for NKdVEs. Additionally, the method is straightforward, significantly reduces the computational effort required to solve NKdVE problems and shows promise for application to a wide range of partial differential equations (PDEs). The efficacy of AHRDTM is illustrated through tables and graphical representations.

Item Type:	Article
Keyword:	Adaptive Multistep Differential Transform Method, Multistep Reduced Differential Transform Method; Korteweg-De Vries Equations, Adaptive Scheme, Adomian Polynomials
Subjects:	Q Science > QA Mathematics > QA1-939 Mathematics > QA299.6-433 Analysis
Department:	FACULTY > Faculty of Science and Natural Resources
Depositing User:	SITI AZIZAH BINTI IDRIS -
Date Deposited:	27 May 2025 16:26
Last Modified:	27 May 2025 16:26
URI:	https://eprints.ums.edu.my/id/eprint/43941

Actions (login required)

View Item