Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order
A new method based on a hybrid of Chebyshev wavelets and finite difference methods is introduced for solving linear and nonlinear fractional differential equations. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/916456 |
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| _version_ | 1832550697972793344 |
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| author | A. Kazemi Nasab A. Kılıçman Z. Pashazadeh Atabakan S. Abbasbandy |
| author_facet | A. Kazemi Nasab A. Kılıçman Z. Pashazadeh Atabakan S. Abbasbandy |
| author_sort | A. Kazemi Nasab |
| collection | DOAJ |
| description | A new method based on a hybrid of Chebyshev wavelets and finite difference methods is introduced for solving linear and nonlinear fractional differential equations. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of linear or nonlinear algebraic equations. This method can be considered as a nonuniform finite difference method. Some examples are given to verify and illustrate the efficiency and simplicity of the proposed method. |
| format | Article |
| id | doaj-art-5f495963df5e427ca3c1652128a5053a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5f495963df5e427ca3c1652128a5053a2025-02-03T06:06:05ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/916456916456Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional OrderA. Kazemi Nasab0A. Kılıçman1Z. Pashazadeh Atabakan2S. Abbasbandy3Department of Mathematics, University Putra Malaysia (UPM), 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics, University Putra Malaysia (UPM), 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics, University Putra Malaysia (UPM), 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics, Imam Khomeini International University, Ghazvin 34149, IranA new method based on a hybrid of Chebyshev wavelets and finite difference methods is introduced for solving linear and nonlinear fractional differential equations. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of linear or nonlinear algebraic equations. This method can be considered as a nonuniform finite difference method. Some examples are given to verify and illustrate the efficiency and simplicity of the proposed method.http://dx.doi.org/10.1155/2013/916456 |
| spellingShingle | A. Kazemi Nasab A. Kılıçman Z. Pashazadeh Atabakan S. Abbasbandy Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order Abstract and Applied Analysis |
| title | Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order |
| title_full | Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order |
| title_fullStr | Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order |
| title_full_unstemmed | Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order |
| title_short | Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order |
| title_sort | chebyshev wavelet finite difference method a new approach for solving initial and boundary value problems of fractional order |
| url | http://dx.doi.org/10.1155/2013/916456 |
| work_keys_str_mv | AT akazeminasab chebyshevwaveletfinitedifferencemethodanewapproachforsolvinginitialandboundaryvalueproblemsoffractionalorder AT akılıcman chebyshevwaveletfinitedifferencemethodanewapproachforsolvinginitialandboundaryvalueproblemsoffractionalorder AT zpashazadehatabakan chebyshevwaveletfinitedifferencemethodanewapproachforsolvinginitialandboundaryvalueproblemsoffractionalorder AT sabbasbandy chebyshevwaveletfinitedifferencemethodanewapproachforsolvinginitialandboundaryvalueproblemsoffractionalorder |