Some implicit methods for the numerical solution of Burgers’ equation

摘要

In this article we develop multisymplectic box methods on Burgers’ equation. Burgers’ equation has some discontinuous solutions because of effects of viscosity term. These discontinuities raise phenomenon of shock waves. Some explicit and implicit numerical methods have been experimented on Burgers’ equation but these schemes have not been seen proper in this case because of their conditional stability and existence of viscosity term. To avoid these problems, multisymplectic box scheme which has been constructed for KdV equation is purposed for Burgers’ equation. Multisymplectic box scheme is a very effective box scheme in diminishing artificial wiggles which appear in approximation solutions. We consider two types of box schemes and implement on Burgers’ equation to get better results with no artificial wiggles.