Time discretizations for evolution problems

Miloslav Vlasák

Applications of Mathematics (2017)

  • Volume: 62, Issue: 2, page 135-169
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Vlasák, Miloslav. "Time discretizations for evolution problems." Applications of Mathematics 62.2 (2017): 135-169. <http://eudml.org/doc/287958>.

@article{Vlasák2017,
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.},
author = {Vlasák, Miloslav},
journal = {Applications of Mathematics},
keywords = {time discretizations; parabolic PDEs; stiff ODEs; Runge-Kutta methods; multi-step methods},
language = {eng},
number = {2},
pages = {135-169},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Time discretizations for evolution problems},
url = {http://eudml.org/doc/287958},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Vlasák, Miloslav
TI - Time discretizations for evolution problems
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 2
SP - 135
EP - 169
AB - 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.
LA - eng
KW - time discretizations; parabolic PDEs; stiff ODEs; Runge-Kutta methods; multi-step methods
UR - http://eudml.org/doc/287958
ER -

References

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