A collocation-shooting method for solving fractional boundary value problems

Qasem M. Al-Mdallal; Muhammed I. Syam; M. N. Anwar

doi:10.1016/j.cnsns.2010.01.020

A collocation-shooting method for solving fractional boundary value problems

Department of Mathematical Sciences

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

123 Citations (Scopus)

Abstract

In this paper, we discuss the numerical solution of special class of fractional boundary value problems of order 2. The method of solution is based on a conjugating collocation and spline analysis combined with shooting method. A theoretical analysis about the existence and uniqueness of exact solution for the present class is proven. Two examples involving Bagley-Torvik equation subject to boundary conditions are also presented; numerical results illustrate the accuracy of the present scheme.

Original language	English
Pages (from-to)	3814-3822
Number of pages	9
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	15
Issue number	12
DOIs	https://doi.org/10.1016/j.cnsns.2010.01.020
Publication status	Published - Dec 2010

Keywords

Bagley-Torvik equation
Collocation method
Shooting method

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Applied Mathematics

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10.1016/j.cnsns.2010.01.020

Cite this

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title = "A collocation-shooting method for solving fractional boundary value problems",

abstract = "In this paper, we discuss the numerical solution of special class of fractional boundary value problems of order 2. The method of solution is based on a conjugating collocation and spline analysis combined with shooting method. A theoretical analysis about the existence and uniqueness of exact solution for the present class is proven. Two examples involving Bagley-Torvik equation subject to boundary conditions are also presented; numerical results illustrate the accuracy of the present scheme.",

keywords = "Bagley-Torvik equation, Collocation method, Shooting method",

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

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 nos. .",

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language = "English",

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T1 - A collocation-shooting method for solving fractional boundary value problems

AU - Al-Mdallal, Qasem M.

AU - Syam, Muhammed I.

AU - Anwar, M. N.

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 nos. .

PY - 2010/12

Y1 - 2010/12

N2 - In this paper, we discuss the numerical solution of special class of fractional boundary value problems of order 2. The method of solution is based on a conjugating collocation and spline analysis combined with shooting method. A theoretical analysis about the existence and uniqueness of exact solution for the present class is proven. Two examples involving Bagley-Torvik equation subject to boundary conditions are also presented; numerical results illustrate the accuracy of the present scheme.

AB - In this paper, we discuss the numerical solution of special class of fractional boundary value problems of order 2. The method of solution is based on a conjugating collocation and spline analysis combined with shooting method. A theoretical analysis about the existence and uniqueness of exact solution for the present class is proven. Two examples involving Bagley-Torvik equation subject to boundary conditions are also presented; numerical results illustrate the accuracy of the present scheme.

KW - Bagley-Torvik equation

KW - Collocation method

KW - Shooting method

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UR - https://www.scopus.com/pages/publications/77952705214#tab=citedBy

U2 - 10.1016/j.cnsns.2010.01.020

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M3 - Article

AN - SCOPUS:77952705214

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VL - 15

SP - 3814

EP - 3822

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 12

ER -

A collocation-shooting method for solving fractional boundary value problems

Abstract

Keywords

ASJC Scopus subject areas

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