Communications in Mathematical Sciences

Volume 11 (2013)

Number 3

A relaxation method for the pulsating traveling front simulations of the periodic advection diffusion reaction equations

Pages: 651 – 678



Min Tang (Institute of Natural Sciences, Jiao Tong University, Shanghai, China)


In this paper, we propose a new relaxation method to study the pulsating traveling front for the one dimensional space and time periodic advection diffusion reaction equations. By introducing an additional parameter depending on time, the front position is confined around a fixed point, so that this method requires small computational domain. Moreover, the time evolution of this additional parameter gives the traveling velocity automatically, and the results of the original advection diffusion reaction equation can be recovered.


space periodic advection diffusion reaction equation, time periodic advection diffusion reaction equation, traveling wave solution, pulsating traveling front, relaxation method

2010 Mathematics Subject Classification

35C07, 35K57, 65M06

Published 14 May 2013