Type I operators and the approximation of singular two-point boundary value problems

Mohamed A. El-Gebeily; Donal O'Regan; Salim Messauodi

doi:10.1016/j.amc.2010.05.020

Type I operators and the approximation of singular two-point boundary value problems

Mohamed A. El-Gebeily^*
, Donal O'Regan
, Salim Messauodi

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Review article › peer-review

Abstract

A class of self adjoint operators associated with second order singular ordinary differential expressions, arises naturally when the problem is weakly formulated and integration by parts is performed. We call this class Type I operators. It turns out that this class can be successfully used to tackle numerical approximations of singular two-point boundary value problems. They can also be approximated by regular differential operators in a straightforward manner without having to bring the delicate structure of singular differential operators to the forefront of the investigation.

Original language	English
Pages (from-to)	3433-3438
Number of pages	6
Journal	Applied Mathematics and Computation
Volume	216
Issue number	12
DOIs	https://doi.org/10.1016/j.amc.2010.05.020
State	Published - 15 Aug 2010

Bibliographical note

Funding Information:
The first author would like to acknowledge the support of King Fahd University under research Grant No. in090029 .

Keywords

Galerkin method
Self adjoint operators
Singular differential equations
Variational equations

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2010.05.020

Cite this

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title = "Type I operators and the approximation of singular two-point boundary value problems",

abstract = "A class of self adjoint operators associated with second order singular ordinary differential expressions, arises naturally when the problem is weakly formulated and integration by parts is performed. We call this class Type I operators. It turns out that this class can be successfully used to tackle numerical approximations of singular two-point boundary value problems. They can also be approximated by regular differential operators in a straightforward manner without having to bring the delicate structure of singular differential operators to the forefront of the investigation.",

keywords = "Galerkin method, Self adjoint operators, Singular differential equations, Variational equations",

author = "El-Gebeily, \{Mohamed A.\} and Donal O'Regan and Salim Messauodi",

note = "Funding Information: The first author would like to acknowledge the support of King Fahd University under research Grant No. in090029 .",

year = "2010",

month = aug,

day = "15",

doi = "10.1016/j.amc.2010.05.020",

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T1 - Type I operators and the approximation of singular two-point boundary value problems

AU - El-Gebeily, Mohamed A.

AU - O'Regan, Donal

AU - Messauodi, Salim

N1 - Funding Information: The first author would like to acknowledge the support of King Fahd University under research Grant No. in090029 .

PY - 2010/8/15

Y1 - 2010/8/15

N2 - A class of self adjoint operators associated with second order singular ordinary differential expressions, arises naturally when the problem is weakly formulated and integration by parts is performed. We call this class Type I operators. It turns out that this class can be successfully used to tackle numerical approximations of singular two-point boundary value problems. They can also be approximated by regular differential operators in a straightforward manner without having to bring the delicate structure of singular differential operators to the forefront of the investigation.

AB - A class of self adjoint operators associated with second order singular ordinary differential expressions, arises naturally when the problem is weakly formulated and integration by parts is performed. We call this class Type I operators. It turns out that this class can be successfully used to tackle numerical approximations of singular two-point boundary value problems. They can also be approximated by regular differential operators in a straightforward manner without having to bring the delicate structure of singular differential operators to the forefront of the investigation.

KW - Galerkin method

KW - Self adjoint operators

KW - Singular differential equations

KW - Variational equations

UR - https://www.scopus.com/pages/publications/77953618197

U2 - 10.1016/j.amc.2010.05.020

DO - 10.1016/j.amc.2010.05.020

M3 - Review article

AN - SCOPUS:77953618197

SN - 0096-3003

VL - 216

SP - 3433

EP - 3438

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 12

ER -

Type I operators and the approximation of singular two-point boundary value problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this