The main purpose of the paper is to show how to use implicit–explicit Runge–Kutta methods in a much more general context than usually found in the literature, obtainingvery effective schemes for a large class of problems. This approach gives a great flexibility,and allows, in many cases the construction of simple linearly implicit schemes without anyNewton’s iteration. This is obtained by identifying the (possibly linear) dependence on theunknown of the system which generates the stiffness. Only the stiff dependence is treatedimplicitly, thenmaking the wholemethod much simpler than fully implicit ones. The resultingschemes are denoted as semi-implicit R–K.We adopt several semi-implicit R–K methods upto order three.We illustrate the effectiveness of the new approach with many applications toreaction–diffusion, convection diffusion and nonlinear diffusion system of equations

High Order Semi-implicit Schemes for Time Dependent Partial Differential Equations

BOSCARINO, SEBASTIANO;RUSSO, Giovanni
2016-01-01

Abstract

The main purpose of the paper is to show how to use implicit–explicit Runge–Kutta methods in a much more general context than usually found in the literature, obtainingvery effective schemes for a large class of problems. This approach gives a great flexibility,and allows, in many cases the construction of simple linearly implicit schemes without anyNewton’s iteration. This is obtained by identifying the (possibly linear) dependence on theunknown of the system which generates the stiffness. Only the stiff dependence is treatedimplicitly, thenmaking the wholemethod much simpler than fully implicit ones. The resultingschemes are denoted as semi-implicit R–K.We adopt several semi-implicit R–K methods upto order three.We illustrate the effectiveness of the new approach with many applications toreaction–diffusion, convection diffusion and nonlinear diffusion system of equations
2016
IMEX schemes ; Stiff problem; Time dependant partial differential equations
File in questo prodotto:
File Dimensione Formato  
BoscFilbetRusso.pdf

solo gestori archivio

Licenza: Non specificato
Dimensione 1.17 MB
Formato Adobe PDF
1.17 MB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/18237
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 77
  • ???jsp.display-item.citation.isi??? 70
social impact