Two different temporal domain integration schemes combined with compact finite difference method to solve modified Burgers’ equation

Abstract

The modified Burgers’ equation has application in various fields such as explosions and sonic boom theory, propagation of torsional waves in thin circular viscoelastic rod, acoustic waves produced by laser radiations, etc. A sixth-order compact finite difference scheme has been used for the space integration. Two different approaches have been followed for time integration. One is the Crank-Nicolson scheme in which the nonlinear term is handled with a quasilinearization process. Another is the strong stability preserving Runge-Kutta method of four stage, third-order convergence (SSP-RK43), in which no linearization is required. The stability analysis for both the schemes has been presented and is shown to be stable. Few test problems have been solved, demonstrating the performance of the proposed techniques. The L2 and L∞ error norms are calculated and are compared with the previous work. The aim of the paper is to solve such an important equation with better accuracy and less computational efforts.

Keywords

• Modified Burgers’ equation
• Compact finite difference scheme
• Crank-Nicolson
• Quasilinearization
• SSP-RK43
• Von-Neumann