Convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument

Hui Liang; Dongyang Shi; Wanjin Lv

doi:10.1016/j.amc.2010.06.028

Convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument

Hui Liang^*
, Dongyang Shi
, Wanjin Lv

^*Corresponding author for this work

Heilongjiang University
Zhengzhou University

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

The paper deals with the convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument. The optimal convergence orders are obtained for the semidiscrete and full discrete (backward Euler) methods respectively. Both the discrete solutions are proved to be asymptotically stable under the condition that the analytical solution is asymptotically stable.

Original language	English
Pages (from-to)	854-860
Number of pages	7
Journal	Applied Mathematics and Computation
Volume	217
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2010.06.028
State	Published - 15 Sep 2010
Externally published	Yes

Keywords

Asymptotic stability
Convergence
Galerkin methods
Partial differential equation
Piecewise constant arguments

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10.1016/j.amc.2010.06.028

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title = "Convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument",

abstract = "The paper deals with the convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument. The optimal convergence orders are obtained for the semidiscrete and full discrete (backward Euler) methods respectively. Both the discrete solutions are proved to be asymptotically stable under the condition that the analytical solution is asymptotically stable.",

keywords = "Asymptotic stability, Convergence, Galerkin methods, Partial differential equation, Piecewise constant arguments",

author = "Hui Liang and Dongyang Shi and Wanjin Lv",

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doi = "10.1016/j.amc.2010.06.028",

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AU - Liang, Hui

AU - Shi, Dongyang

AU - Lv, Wanjin

PY - 2010/9/15

Y1 - 2010/9/15

N2 - The paper deals with the convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument. The optimal convergence orders are obtained for the semidiscrete and full discrete (backward Euler) methods respectively. Both the discrete solutions are proved to be asymptotically stable under the condition that the analytical solution is asymptotically stable.

AB - The paper deals with the convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument. The optimal convergence orders are obtained for the semidiscrete and full discrete (backward Euler) methods respectively. Both the discrete solutions are proved to be asymptotically stable under the condition that the analytical solution is asymptotically stable.

KW - Asymptotic stability

KW - Convergence

KW - Galerkin methods

KW - Partial differential equation

KW - Piecewise constant arguments

UR - https://www.scopus.com/pages/publications/77955661652

U2 - 10.1016/j.amc.2010.06.028

DO - 10.1016/j.amc.2010.06.028

M3 - 文章

AN - SCOPUS:77955661652

SN - 0096-3003

VL - 217

SP - 854

EP - 860

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument

Abstract

Keywords

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