Numerical Solution of Fisher's Equation Using a Moving Mesh Method

The paper investigates the viability of using moving mesh methods to simulate travelling wave solutions of Fisher's equation. Results are presented that illustrate the weaknesses in moving mesh methods based on equidistribution of some popular monitor functions. It is shown that knowledge of the differential equation and the travelling wave solution may be used to construct a monitor function that yields accurate results with suitably chosen moving mesh methods. A comparison is made between a moving mesh partial differential equation and a moving mesh differential-algebraic equation for the evolution in time.