Applications of Mathematics, Vol. 62, No. 2, pp. 135-169, 2017
Time discretizations for evolution problems
Received September 26, 2016. First published March 6, 2017.
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.
Affiliations: Miloslav Vlasák, Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, 186 75 Praha 8, Czech Republic, e-mail: firstname.lastname@example.org