Two-stage interval Krawczyk-Schwarz methods with applications to nonlinear parabolic PDE

Abstract

By using interval techniques, it is possible to obtain global convergence properties and verified enclosures in the numerical solution of several classes of nonlinear systems of equations. In the present paper, we introduce Newton-like interval methods of the so-called Krawczyktype for systems arizing from discretizations of almost linear parabolic problems. Parallelism is introduced by domain decomposition and an adaptation of the Schwarz Alternating Procedure. Numerical results from a Sun Opteron cluster are included. © Springer-Verlag Berlin Heidelberg 2007.