Work

A Linear Time-space High-order Compact Finite Difference Scheme for Solving the One-dimensional Nonlinear Burgers' Equation

Year: 2025

Type: article

Abstract: This paper presents a novel finite difference scheme for solving the one-dimensional (1D) nonlinear Burgers' equation with high accuracy. A fourth-order backward difference formula is employed to discretize the time derivative, while the nonlinear residual terms are efficiently linearized via Taylor series expansion. Spatial discretization is achieved using a fourth-order compact difference scheme for second-order derivatives and a fourth-order Padé scheme for first-order derivatives. As a result, the proposed approach yields a linear compact finite difference scheme with fourth-order accuracy in both temporal and spatial dimensions. The accuracy and stability of this method are demonstrated through a series of numerical experiments, validating its effectiveness for solving nonlinear Burgers' equations. The high-order finite difference scheme for the nonlinear Burgers' equation can accurately simulate phenomena in fields such as physics, sound wave propagation, and aerodynamics.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240527

Authors: Xueqing Miao, Jiaye Gan, Tingfu Ma, Lili Wu

Institutions: Ningxia Normal University, Wuhan University

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Natural Science Foundation of Ningxia Province, Key Research and Development Program of Ningxia

Awards: G4835478390, G5864829281, G7651696723