Contractivity of θ-method for semi-discrete systems
Luciano Galeone, Carmela Mastroserio · Numerical Methods for Partial Differential Equations · 1996
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.