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.

Cavalli, F., Semplice, M., High Order Relaxed Schemes for Nonlinear Reaction Diffusion Problems, Contributed paper, in SIMAI 2006, (Ragusa, 22-26 May 2006), SIMAI, Ragusa 2007: N/A-N/A [http://hdl.handle.net/10807/85651]

High Order Relaxed Schemes for Nonlinear Reaction Diffusion Problems

Cavalli;
2007

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.
Inglese
SIMAI 2006
SIMAI
Ragusa
Contributed paper
22-mag-2006
26-mag-2006
SIMAI
Cavalli, F., Semplice, M., High Order Relaxed Schemes for Nonlinear Reaction Diffusion Problems, Contributed paper, in SIMAI 2006, (Ragusa, 22-26 May 2006), SIMAI, Ragusa 2007: N/A-N/A [http://hdl.handle.net/10807/85651]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/85651
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