Premium
Contractivity of θ‐method for semi‐discrete systems
Author(s) -
Galeone Luciano,
Mastroserio Carmela
Publication year - 1996
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199609)12:5<615::aid-num5>3.0.co;2-n
Subject(s) - jacobian matrix and determinant , mathematics , discretization , nonlinear system , diagonal matrix , diagonal , galerkin method , partial differential equation , matrix (chemical analysis) , mathematical analysis , norm (philosophy) , geometry , law , physics , materials science , quantum mechanics , political science , composite material
We consider nonlinear semi‐discrete problems that derive by reaction diffusion systems of partial differential equations, when finite difference methods or Faedo Galerkin methods are used for spatial discretization. The aim of this article is to give sufficient conditions for the contractivity of the θ‐method, in a norm generated by a positive diagonal matrix G . We show that the numerical contractivity property is obtained if some matrices, constructed by means of the Jacobian matrix of nonlinear term, are M ‐matrices. © 1996 John Wiley & Sons, Inc.