Chebyshev Finite Difference Method for Fractional Boundary Value Problems
This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving bounda...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Islamic Azad University
2015-09-01
|
| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/316/231 |
| _version_ | 1818821151158173696 |
|---|---|
| author | Boundary |
| author_facet | Boundary |
| author_sort | Boundary |
| collection | DOAJ |
| description | This paper presents a numerical method for fractional differential
equations using Chebyshev finite difference method. The fractional
derivatives are described in the Caputo sense. Numerical results
show that this method is of high accuracy and is more convenient and
efficient for solving boundary value problems involving fractional ordinary
differential equations.
AMS Subject Classification: 34A08
Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points,
fractional differential equation, finite difference
1. Introduction
The idea of a derivative which interpolates between the familiar integer
order derivatives was introduced many years ago and has gained
increasing importance only in recent years due to the development of
mathematical models of a certain situations in engineering, materials
science, control theory, polymer modelling etc. For example see [20, 22,
25, 26].
Most fractional order differential equations describing real life situations,
in general do not have exact analytical solutions. Several numerical
and approximate analytical methods for ordinary differential equation
Received: December 2014; Accepted: March 2015
57
Journal of Mathematical Extension
Vol. 9, No. 3, (2015), 57-71
ISSN: 1735-8299
URL: http://www.ijmex.com
Chebyshev Finite Difference Method for
Fractional Boundary Value Problems
H. Azizi
Taft Branch, Islamic Azad University
Abstract. This paper presents a numerical method for fractional differential
equations using Chebyshev finite difference method. The fractional
derivative |
| first_indexed | 2024-12-18T23:03:37Z |
| format | Article |
| id | doaj.art-1dcdd837aa954833806e9d7ca6c1d625 |
| institution | Directory Open Access Journal |
| issn | 1735-8299 1735-8299 |
| language | English |
| last_indexed | 2024-12-18T23:03:37Z |
| publishDate | 2015-09-01 |
| publisher | Islamic Azad University |
| record_format | Article |
| series | Journal of Mathematical Extension |
| spelling | doaj.art-1dcdd837aa954833806e9d7ca6c1d6252022-12-21T20:48:30ZengIslamic Azad UniversityJournal of Mathematical Extension1735-82991735-82992015-09-01935771Chebyshev Finite Difference Method for Fractional Boundary Value ProblemsBoundary0Taft Branch, Islamic Azad UniversityThis paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015), 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivativehttp://ijmex.com/index.php/ijmex/article/view/316/231 |
| spellingShingle | Boundary Chebyshev Finite Difference Method for Fractional Boundary Value Problems Journal of Mathematical Extension |
| title | Chebyshev Finite Difference Method for Fractional Boundary Value Problems |
| title_full | Chebyshev Finite Difference Method for Fractional Boundary Value Problems |
| title_fullStr | Chebyshev Finite Difference Method for Fractional Boundary Value Problems |
| title_full_unstemmed | Chebyshev Finite Difference Method for Fractional Boundary Value Problems |
| title_short | Chebyshev Finite Difference Method for Fractional Boundary Value Problems |
| title_sort | chebyshev finite difference method for fractional boundary value problems |
| url | http://ijmex.com/index.php/ijmex/article/view/316/231 |
| work_keys_str_mv | AT boundary chebyshevfinitedifferencemethodforfractionalboundaryvalueproblems |