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Applications of Mathematics

, Volume 62, Issue 2, pp 135–169 | Cite as

Time discretizations for evolution problems

  • Miloslav Vlasák
Article
  • 73 Downloads

Abstract

The aim of this work is to give an introductory survey on time discretizations for liner parabolic problems. The theory of stability for stiff ordinary differential equations is explained on this problem and applied to Runge-Kutta and multi-step discretizations. Moreover, a natural connection between Galerkin time discretizations and Runge-Kutta methods together with order reduction phenomenon is discussed.

Keywords

time discretizations parabolic PDEs stiff ODEs Runge-Kutta methods multi-step methods 

MSC 2010

65J10 65L04 65L20 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of Mathematical AnalysisCharles University, Faculty of Mathematics and PhysicsPraha 8Czech Republic

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