High Order Relaxed Schemes for Nonlinear Reaction Diffusion Problems

Fausto Cavalli, M. Semplice

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto diffusive relaxed schemes for the numer- ical approximation of nonlinear reaction diffusion equations. High order methods are obtained by coupling ENO and WENO schemes for space discretization with IMEX schemes for time integration, where the implicit part can be explicitly solved at a linear cost. To illustrate the high accuracy and good properties of the proposed numericalschemes, also in the degenerate case, we consider various examples in one and two dimensions: the Fisher-Kolmogoroff equation, the porous-Fisher equation and the porous medium equation with strong absorption.
Original languageEnglish
Title of host publicationSIMAI 2006
PagesN/A
Number of pages10
Publication statusPublished - 2007
EventSIMAI - Ragusa
Duration: 22 May 200626 May 2006

Conference

ConferenceSIMAI
CityRagusa
Period22/5/0626/5/06

Keywords

  • relaxation schemes

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