论文信息 - A nonstandard difference-integral method for the viscous Burgers' equation

A nonstandard difference-integral method for the viscous Burgers' equation

We develop a nonstandard difference-integral method based on a nonstandard finite difference method coupled with a CE–SE scheme. We use the viscous Burgers’ equation with preestablished conditions as a benchmark for testing our method. Numerical results obtained show that this new method is more robust and efficient than the associated standard difference-integral method. 2007 Elsevier Inc. All rights reserved.

Silvia Jerez Galiano

[1] José Vicente Romero,et al. A semi-implicit space-time CE-SE method to improve mass conservation through tapered ducts in internal combustion engines , 2004, Math. Comput. Model..

[2] R. Mickens. Applications of nonstandard finite difference schemes , 2000 .

[3] D. Kröner. Numerical Schemes for Conservation Laws , 1997 .

[4] E. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[5] Francisco J. Solis,et al. Nonstandard discrete approximationspreserving stability properties of continuous mathematical models , 2004, Math. Comput. Model..

[6] Sin-Chung Chang,et al. The Space-Time Conservation Element and Solution Element Method-A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 2; Numerical Simulation of Shock Waves and Contact Discontinuities , 1998 .

[7] Francisco José Arnau,et al. Analysis of numerical methods to solve one-dimensional fluid-dynamic governing equations under impulsive flow in tapered ducts , 2004 .

[8] STEPHEN F. DAVISt. A Simplified TVD Finite Difference Scheme Via Artificial Viscosity A SIMPLIFIED TVD FINITE DIFFERENCE SCHEME VIA ARTIFICIAL VISCOSITY , .