Numerical solution of reaction–diffusion systems of λλ–ωω type by trigonometrically fitted methods

The numerical solution of reaction–diffusion equations of λλ–ωω type, which are known to possess a one-parameter family of periodic plane wave solutions, is object of this paper. Due to the periodic character of such solutions, a special purpose numerical integration is here proposed, based on adapted finite differences. The adaptation occurs at the level of the problem, by a suitable spatial semi-discretization based on trigonometrically fitted finite differences. Numerical experiments confirming the effectiveness of the approach are given.