ORIGINAL RESEARCH article
Front. Phys.
Sec. Statistical and Computational Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1631259
An efficient explicit group method for time fractional Burgers equation
Provisionally accepted
- King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
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Fractional Burgers-type equations are essential mathematical models for describing the cumulative effect of wall friction through boundary layer along with the unidirectional propagation of weakly nonlinear acoustic waves. It is a major challenge to develop efficient, stable, and accurate numerical schemes that simulate the corresponding physical complex phenomena, owing to the nonlinearity and nonlocality properties in these equations. The objective of this article is to design a linearized modified fractional explicit group method for solving the twodimensional time fractional Burgers equation with suitable initial and boundary conditions. For the construction of the proposed method, the L 1 discretization formula is used for dealing with the fractional temporal derivative, whereas a linearized difference scheme on a coarse mesh is employed to approximate the derivatives in space direction. Meanwhile, a linearized Crank Nicolson difference method is formulated for checking the efficiency of the proposed method. The stability and convergence of the presented methods are studied and proven thoroughly. Numerical simulations are performed and numerical results are reported in terms of error norm and CPU time, from which it is shown that the linearized grouping method reduces computing time by 70-90% while maintaining comparable accuracy compared to the linearized Crank-Nicolson method in dealing with the time fractional Burgers model.
Keywords: Burgers equation, Caputo fractional derivative, Explicit group methods, Finite differences, Stability and convergence, numerical simulation
Received: 19 May 2025; Accepted: 23 Jun 2025.
Copyright: © 2025 Salama. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Fouad Mohammad Salama, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
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