Sixth-order conservative compact difference schemes for the generalized Burgers’ equation
Abstract
Abstract In this paper, two finite difference schemes with second-order temporal accuracy and sixth-order spatial accuracy are proposed for the generalized Burgers’ equation. A two-level nonlinear scheme and a three-level linearized scheme are constructed under periodic boundary conditions. The solvability, discrete energy conservation, and convergence of the schemes are rigorously analyzed. In particular, convergence in the discrete L ∞ -norm is established by using a cut-off function technique. Numerical results confirm the theoretical accuracy and illustrate the performance of the proposed schemes.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Numerical methods for differential equations
Differential Equations and Numerical Methods
Publication details
- Journal / source
- Physica Scripta
- Publisher
- IOP Publishing
- Volume
- 101
- Issue
- 21
- Pages
- 215201–215201
- Publication date
- 21 May 2026