Numerical solution of reaction-diffusion systems of λ-ω Type by trigonometrically fitted methods

The numerical solution of reaction-diffusion equations of λ-ω 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.