Matrix stability of the difference schemes for nonlocal boundary value problems for parabolic differential equations

Ibrahim Karatay; Şerife Rabia Bayramoglu; Bahattin Yildiz; Bulent Kokluce

Matrix stability of the difference schemes for nonlocal boundary value problems for parabolic differential equations

Ibrahim Karatay, Şerife Rabia Bayramoglu, Bahattin Yildiz, Bulent Kokluce

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

Abstract

In this work, a first order and second order difference schemes, namely Rothe and Crank-Nicholson, respectively, for solving nonlocal boundary value problems for parabolic differential equations are presented. The stability of the difference schemes are proved by using the matrix stability approach. Numerical results are provided to illustrate the accuracy and efficiency of the schemes.

Original language	English (US)
Pages (from-to)	819-827
Number of pages	9
Journal	International Journal of Physical Sciences
Volume	6
Issue number	4
State	Published - Feb 18 2011
Externally published	Yes

Keywords

Crank-Nicholson difference scheme
Kailath Theorem
Matrix block inversion
Matrix stability
Nonlocal boundary value problems for parabolic differential equations
Rothe difference scheme
Schur complement

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
General Physics and Astronomy

Cite this

@article{729a86c9bce94e31a65d104eacdd7fda,

title = "Matrix stability of the difference schemes for nonlocal boundary value problems for parabolic differential equations",

abstract = "In this work, a first order and second order difference schemes, namely Rothe and Crank-Nicholson, respectively, for solving nonlocal boundary value problems for parabolic differential equations are presented. The stability of the difference schemes are proved by using the matrix stability approach. Numerical results are provided to illustrate the accuracy and efficiency of the schemes.",

keywords = "Crank-Nicholson difference scheme, Kailath Theorem, Matrix block inversion, Matrix stability, Nonlocal boundary value problems for parabolic differential equations, Rothe difference scheme, Schur complement",

author = "Ibrahim Karatay and Bayramoglu, {{\c S}erife Rabia} and Bahattin Yildiz and Bulent Kokluce",

year = "2011",

month = feb,

day = "18",

language = "English (US)",

volume = "6",

pages = "819--827",

journal = "International Journal of Physical Sciences",

issn = "1992-1950",

publisher = "Academic Journals",

number = "4",

}

TY - JOUR

T1 - Matrix stability of the difference schemes for nonlocal boundary value problems for parabolic differential equations

AU - Karatay, Ibrahim

AU - Bayramoglu, Şerife Rabia

AU - Yildiz, Bahattin

AU - Kokluce, Bulent

PY - 2011/2/18

Y1 - 2011/2/18

N2 - In this work, a first order and second order difference schemes, namely Rothe and Crank-Nicholson, respectively, for solving nonlocal boundary value problems for parabolic differential equations are presented. The stability of the difference schemes are proved by using the matrix stability approach. Numerical results are provided to illustrate the accuracy and efficiency of the schemes.

AB - In this work, a first order and second order difference schemes, namely Rothe and Crank-Nicholson, respectively, for solving nonlocal boundary value problems for parabolic differential equations are presented. The stability of the difference schemes are proved by using the matrix stability approach. Numerical results are provided to illustrate the accuracy and efficiency of the schemes.

KW - Crank-Nicholson difference scheme

KW - Kailath Theorem

KW - Matrix block inversion

KW - Matrix stability

KW - Nonlocal boundary value problems for parabolic differential equations

KW - Rothe difference scheme

KW - Schur complement

UR - http://www.scopus.com/inward/record.url?scp=79957529792&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957529792&partnerID=8YFLogxK

M3 - Article

SN - 1992-1950

VL - 6

SP - 819

EP - 827

JO - International Journal of Physical Sciences

JF - International Journal of Physical Sciences

IS - 4

ER -

Matrix stability of the difference schemes for nonlocal boundary value problems for parabolic differential equations

Abstract

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this