The treatise is focused on the numerical solution of lamda-omega reaction-diffusion problems, by means of a suitably adapted method of lines. Due to the non linearity of the vector field and the oscillatory behaviour of the solution, we propose to combine a spatial semidiscretization of the operator through trigonometrically fitted finite differences with an IMEX integration in time. Accuracy and stability properties of the overall numerical scheme are proved and experiments confirming the effectiveness of the approach are also provided.
Adapted IMEX numerical methods for reaction-diffusion problems
Martina Moccaldi;Beatrice Paternoster
2019
Abstract
The treatise is focused on the numerical solution of lamda-omega reaction-diffusion problems, by means of a suitably adapted method of lines. Due to the non linearity of the vector field and the oscillatory behaviour of the solution, we propose to combine a spatial semidiscretization of the operator through trigonometrically fitted finite differences with an IMEX integration in time. Accuracy and stability properties of the overall numerical scheme are proved and experiments confirming the effectiveness of the approach are also provided.File in questo prodotto:
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