Time discretizations for evolution problems

• ID: 2748, RIV: 10361048
• ISSN: 0862-7940, ISBN: not specified
• source: Applications of Mathematics
• keywords: time discretizations; parabolic PDEs; stiff ODEs; Runge-Kutta methods; multi-step methods
• authors: Miloslav Vlasák
• authors from KNM: not assigned

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.