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

• Published in: AL-Rafidain journal of computer sciences and mathematics Vol. 17; no. 2; pp. 105 - 109
• Main Authors: almutasim Hamed, Ekhlass Al-Rawi
• Format: Journal Article
• Language: Arabic
• Published: Mosul University 01-12-2023
• Subjects: adomian polynomial; caputo sense; fkdv-b equation; grünwald-letnikov; hybrid finite difference
• ISSN: 1815-4816; 2311-7990
• DOI: 10.33899/csmj.2023.141335.1075

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.