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Time discretizations for evolution problems. (English) Zbl 1424.65070
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
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