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Two-Stage Interval Krawczyk-Schwarz Methods with Applications to Nonlinear Parabolic PDE

  • Hartmut Schwandt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4707)

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 Krawczyk-type 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.

Keywords

almost linear parabolic problems enclosure methods nonlinear systems of equations Newton-like methods Krawczyk operator Schwarz Alternating Procedure domain decomposition parallel methods 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Hartmut Schwandt
    • 1
  1. 1.Technische Universität Berlin, Fakultät II, Institut für Mathematik, MA 6-4, D-10623 BerlinGermany

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