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On the long‐time stability of a backward Euler scheme for Burgers' equation with polynomial force
Author(s) -
Djoko J.K.
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20323
Subject(s) - mathematics , discretization , backward euler method , burgers' equation , polynomial , nonlinear system , euler's formula , partial differential equation , stability (learning theory) , sequence (biology) , mathematical analysis , work (physics) , scheme (mathematics) , mechanical engineering , physics , quantum mechanics , machine learning , biology , computer science , engineering , genetics
In this work we examine the stability of a finite difference approximation for Burgers' equation. More precisely, we consider a Backward Euler discretization scheme in time and approximated the nonlinear term by a linear expression using techniques from 15. The boundedness of the solution sequence with respect to Δ t for t ε [0,∞) is proved with the help of the discrete Gronwall lemmas. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008