An efficient method for solving non-linear singularly perturbed two points boundary-value problems of fractional order

Qasem M. Al-Mdallal; Muhammed I. Syam

doi:10.1016/j.cnsns.2011.10.003

An efficient method for solving non-linear singularly perturbed two points boundary-value problems of fractional order

Department of Mathematical Sciences

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

34 Citations (Scopus)

Abstract

In this paper, we discuss a numerical solution of a class of non-linear fractional singularly perturbed two points boundary-value problem. The method of solution consists of solving reduced problem and boundary layer correction problem. A series method is used to solve the boundary layer correction problem, and then the series solutions is approximated by the Pade' approximant of order [m, m]. Some theoretical results are established and proved. Two numerical examples are discussed to illustrate the efficiency of the present scheme.

Original language	English
Pages (from-to)	2299-2308
Number of pages	10
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	17
Issue number	6
DOIs	https://doi.org/10.1016/j.cnsns.2011.10.003
Publication status	Published - Jun 2012

Keywords

Boundary layer
Boundary layer correction
Fractional derivative
Pade' approximation
Singularly perturbed boundary-value problems

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Applied Mathematics

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10.1016/j.cnsns.2011.10.003

Cite this

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title = "An efficient method for solving non-linear singularly perturbed two points boundary-value problems of fractional order",

abstract = "In this paper, we discuss a numerical solution of a class of non-linear fractional singularly perturbed two points boundary-value problem. The method of solution consists of solving reduced problem and boundary layer correction problem. A series method is used to solve the boundary layer correction problem, and then the series solutions is approximated by the Pade' approximant of order [m, m]. Some theoretical results are established and proved. Two numerical examples are discussed to illustrate the efficiency of the present scheme.",

keywords = "Boundary layer, Boundary layer correction, Fractional derivative, Pade' approximation, Singularly perturbed boundary-value problems",

author = "Al-Mdallal, \{Qasem M.\} and Syam, \{Muhammed I.\}",

note = "Funding Information: The authors would like to express their appreciation for the valuable comments of the reviewers. The authors also would like to express their sincere appreciation to the United Arab Emirates University Research Affairs for the financial support of Grant No. 1643-02-01-10 .",

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AU - Al-Mdallal, Qasem M.

AU - Syam, Muhammed I.

N1 - Funding Information: The authors would like to express their appreciation for the valuable comments of the reviewers. The authors also would like to express their sincere appreciation to the United Arab Emirates University Research Affairs for the financial support of Grant No. 1643-02-01-10 .

PY - 2012/6

Y1 - 2012/6

N2 - In this paper, we discuss a numerical solution of a class of non-linear fractional singularly perturbed two points boundary-value problem. The method of solution consists of solving reduced problem and boundary layer correction problem. A series method is used to solve the boundary layer correction problem, and then the series solutions is approximated by the Pade' approximant of order [m, m]. Some theoretical results are established and proved. Two numerical examples are discussed to illustrate the efficiency of the present scheme.

AB - In this paper, we discuss a numerical solution of a class of non-linear fractional singularly perturbed two points boundary-value problem. The method of solution consists of solving reduced problem and boundary layer correction problem. A series method is used to solve the boundary layer correction problem, and then the series solutions is approximated by the Pade' approximant of order [m, m]. Some theoretical results are established and proved. Two numerical examples are discussed to illustrate the efficiency of the present scheme.

KW - Boundary layer

KW - Boundary layer correction

KW - Fractional derivative

KW - Pade' approximation

KW - Singularly perturbed boundary-value problems

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M3 - Article

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JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 6

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An efficient method for solving non-linear singularly perturbed two points boundary-value problems of fractional order

Abstract

Keywords

ASJC Scopus subject areas

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