The numerical solution of reaction-diffusion equations of λ-Ï 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.
Numerical solution of reaction-diffusion systems of λ-Ï Type by trigonometrically fitted methods
D'Ambrosio, Raffaele;
2016-01-01
Abstract
The numerical solution of reaction-diffusion equations of λ-Ï 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.File in questo prodotto:
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