Stability of θ-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments

Hui Liang; M. Z. Liu; Wanjin Lv

doi:10.1016/j.aml.2009.09.012

Stability of θ-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments

Hui Liang^*
, M. Z. Liu
, Wanjin Lv

^*Corresponding author for this work

Heilongjiang University
Harbin Institute of Technology

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

44 Scopus citations

Abstract

A finite difference method, namely the θ-scheme, is used to solve a partial differential equation with piecewise continuous arguments. First, an example is given to show that the results for original PDEs do not hold for PDEs with piecewise continuous arguments. Next, for the mesh ratio satisfying certain conditions, the stability of this scheme is obtained.

Original language	English
Pages (from-to)	198-206
Number of pages	9
Journal	Applied Mathematics Letters
Volume	23
Issue number	2
DOIs	https://doi.org/10.1016/j.aml.2009.09.012
State	Published - Feb 2010
Externally published	Yes

Keywords

Asymptotic stability
Finite difference method
PDEs
Piecewise continuous arguments
θ-scheme

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10.1016/j.aml.2009.09.012

Cite this

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title = "Stability of θ-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments",

abstract = "A finite difference method, namely the θ-scheme, is used to solve a partial differential equation with piecewise continuous arguments. First, an example is given to show that the results for original PDEs do not hold for PDEs with piecewise continuous arguments. Next, for the mesh ratio satisfying certain conditions, the stability of this scheme is obtained.",

keywords = "Asymptotic stability, Finite difference method, PDEs, Piecewise continuous arguments, θ-scheme",

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doi = "10.1016/j.aml.2009.09.012",

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AU - Liang, Hui

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AU - Lv, Wanjin

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AB - A finite difference method, namely the θ-scheme, is used to solve a partial differential equation with piecewise continuous arguments. First, an example is given to show that the results for original PDEs do not hold for PDEs with piecewise continuous arguments. Next, for the mesh ratio satisfying certain conditions, the stability of this scheme is obtained.

KW - Asymptotic stability

KW - Finite difference method

KW - PDEs

KW - Piecewise continuous arguments

KW - θ-scheme

UR - https://www.scopus.com/pages/publications/70350719221

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DO - 10.1016/j.aml.2009.09.012

M3 - 文章

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EP - 206

JO - Applied Mathematics Letters

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ER -

Stability of θ-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments

Abstract

Keywords

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