Article ID Journal Published Year Pages File Type
4641132 Journal of Computational and Applied Mathematics 2009 10 Pages PDF
Abstract

Reaction–diffusion equations are commonly used in different science and engineering fields to describe spatial patterns arising from the interaction of chemical or biochemical reactions and diffusive transport mechanisms. In this work we design, in a systematic way, non-standard finite-differences (FD) schemes for a class of reaction–diffusion equations of the form 1xσddx(xσdudx)=f(u(x)), x∈[0,1]x∈[0,1], where σσ is the shape power that accounts for the complexity of the domain geometry. The proposed FD scheme, that is derived from a Green’s function formulation, replicates the underlying geometry and reduces to traditional FD schemes for sufficiently small values of the grid spacing. Numerical results show that the non-standard FD scheme offers smaller approximation errors with respect to traditional schemes, specially for coarse grids.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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