Numerical Solutions for Fractional Burgers’ Equation Based on Laplace Transform
Year: 2025
Author: Weiye Sun, Yulian An, Yijin Gao, Songting Luo
Journal of Nonlinear Modeling and Analysis, Vol. 7 (2025), Iss. 1 : pp. 318–333
Abstract
The Burgers’ equation has widespread applications across various fields. In this paper, we propose an efficient approach for obtaining the numerical solution to the time-fractional Burgers’ equation. We extend the classical Burgers’ equation to its fractional form by introducing Caputo derivatives. Using the Cole-Hopf transform, we reformulate the problem into a fractional diffusion equation. The Laplace transform method is then applied to convert the equation into an ordinary differential equation (ODE), which can be solved analytically. However, due to the lack of an inverse Laplace transform for this specific form, numerical approximation methods are then utilised to approximate the true solution. Numerical simulations are provided to demonstrate the stability and accuracy of the proposed method.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2025.318
Journal of Nonlinear Modeling and Analysis, Vol. 7 (2025), Iss. 1 : pp. 318–333
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Fractional Burgers’ equation Laplace transform Caputo derivative numerical simulations.
Author Details
Weiye Sun Email
Yulian An Email
Yijin Gao Email
Songting Luo Email