A numerical study of stiffness effects on some high order splitting methods

In this paper we compare operator splitting methods of first, second, third and fourth orders that are applied to problems with stiff matrices.In order to efficiently solve the resultant subproblems is necessary to use implicit Runge-Kutta methods. It is known that, in this context, the precision or...

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Bibliographic Details
Authors: J. Salcedo-Ruiz, F. J. Sánchez-Bernabé
Format: article
Status:Published version
Publication Date:2006
Country:México
Institution:Universidad Autónoma Metropolitana
Repository:Redalyc-UAM
OAI Identifier:oai:redalyc.org:57065005
Online Access:https://www.redalyc.org/articulo.oa?id=57065005
Access Level:Open access
Keyword:Física, Astronomía y Matemáticas
stiff matrix
Kutta methods
implicit Runge
Operator splitting
Richardson extrapolation
Description
Summary:In this paper we compare operator splitting methods of first, second, third and fourth orders that are applied to problems with stiff matrices.In order to efficiently solve the resultant subproblems is necessary to use implicit Runge-Kutta methods. It is known that, in this context, the precision order of operator splitting schemes is reduced. Furthermore, we propose a fifth order operator splitting method that is obtained by applying Richardson extrapolation to a fourth order method. All methods are tested with a model problem with matrices such that its condition number is taken up to 20,000. Our conclusion is that order reduction is more severe for low order operator splitting methods.