Hybrid Finite Differences Technique for Solving the Nonlinear Fractional Korteweg-De Vries-Burger Equation

Hamed, Almutasim Abdulmuhsin; Al-Rawi, Ekhlass S.

doi:10.33899/csmj.2023.141335.1075

	Hybrid Finite Differences Technique for Solving the Nonlinear Fractional Korteweg-De Vries-Burger Equation
AL-Rafidain Journal of Computer Sciences and Mathematics
Volume 17, Issue 2, December 2023, Pages 105-109 PDF (731.42 K)
Document Type: Research Paper
DOI: 10.33899/csmj.2023.141335.1075
Authors
almutasim Abdulmuhsin Hamed^* ¹; Ekhlass S. Al-Rawi²
¹Department of mathematics, College of computer science and mathematics, University of Mosul
²College of Computer Sciences and Mathematics University of Mosul, Mosul, Iraq
Abstract
This study presents a new algorithm for effectively solving the nonlinear fractional Korteweg-de Vries-Burger equation (NFKDV-B) using a hybrid explicit finite difference technique with the Adomian polynomial (HEFD). The suggested technique addresses the problem of accurately solving the FKDV-B equation with fractional nonlinear space derivatives in numerical solutions. Numerical results are obtained by comparing the exact solution with absolute and mean square errors. The fractional time and space derivatives are estimated using two widely used techniques: the Caputo derivative and the shifted Grünwald-Letnikov (G-L) formulas. Using a test problem to asses the HEFD method accuracy against the exact solution and the conventional explicit finite difference (EFD) method. The results exhibit excellent agreement between the approximate and exact solutions at different time values. The findings highlight the effectiveness of the proposed method across a range of fractional derivative values when compared to the exact solution and conventional explicit finite difference methods.
Keywords
Hybrid finite difference; FKDV-B equation; Adomian polynomial; Caputo sense; Grünwald-Letnikov

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