Geodesic
Time discretizations for evolution problems
Applications of Mathematics, Tome 62 (2017) no. 2, pp. 135-169.

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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.
DOI : 10.21136/AM.2017.0268-16
Classification : 65J08, 65J10, 65L04, 65L20
Keywords: time discretizations; parabolic PDEs; stiff ODEs; Runge-Kutta methods; multi-step methods 
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     title = {Time discretizations for evolution problems},
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Vlasák, Miloslav. Time discretizations for evolution problems. Applications of Mathematics, Tome 62 (2017) no. 2, pp. 135-169. doi : 10.21136/AM.2017.0268-16. http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0268-16/

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