Time discretizations for evolution problems. (English) Zbl 1424.65070

Vlasák, Miloslav

Appl. Math., Praha 62, No. 2, 135-169 (2017).

Summary: 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.

MSC:

65J08	Numerical solutions to abstract evolution equations
65L04	Numerical methods for stiff equations
65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations

Keywords:

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