Direct Method to Solve Differential-Algebraic Equations by Using the Operational Matrices of Chebyshev Cardinal Functions
A new and effective direct method to determine the numerical solution of linear and nonlinear differential-algebraic equations (DAEs) is proposed. The method consists of expanding the required approximate solution as the elements of Chebyshev cardinal functions. The operational matrices for the...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Islamic Azad University
2013-05-01
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| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/196/118 |
| _version_ | 1819153943526113280 |
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| author | M. Heydari G. Barid Loghmani S. M. Hosseini S. M. Karbassi |
| author_facet | M. Heydari G. Barid Loghmani S. M. Hosseini S. M. Karbassi |
| author_sort | M. Heydari |
| collection | DOAJ |
| description | A new and effective direct method to determine the numerical
solution of linear and nonlinear differential-algebraic equations
(DAEs) is proposed. The method consists of expanding the required approximate
solution as the elements of Chebyshev cardinal functions. The
operational matrices for the integration and product of the Chebyshev
cardinal functions are presented. A general procedure for forming these
matrices is given. These matrices play an important role in modelling of
problems. By using these operational matrices together, a differentialalgebraic
equation can be transformed to a system of algebraic equations.
Illustrative examples are included to demonstrate the validity and
applicability of the technique |
| first_indexed | 2024-12-22T15:13:13Z |
| format | Article |
| id | doaj.art-428e96b516214cd29e517718f40d6919 |
| institution | Directory Open Access Journal |
| issn | 1735-8299 1735-8299 |
| language | English |
| last_indexed | 2024-12-22T15:13:13Z |
| publishDate | 2013-05-01 |
| publisher | Islamic Azad University |
| record_format | Article |
| series | Journal of Mathematical Extension |
| spelling | doaj.art-428e96b516214cd29e517718f40d69192022-12-21T18:21:49ZengIslamic Azad UniversityJournal of Mathematical Extension1735-82991735-82992013-05-01722547Direct Method to Solve Differential-Algebraic Equations by Using the Operational Matrices of Chebyshev Cardinal FunctionsM. Heydari0G. Barid Loghmani1S. M. Hosseini2S. M. Karbassi3Yazd UniversityYazd UniversityKhatam Center, Islamic Azad University Khatam, YazdIslamic Azad University, Yazd BranchA new and effective direct method to determine the numerical solution of linear and nonlinear differential-algebraic equations (DAEs) is proposed. The method consists of expanding the required approximate solution as the elements of Chebyshev cardinal functions. The operational matrices for the integration and product of the Chebyshev cardinal functions are presented. A general procedure for forming these matrices is given. These matrices play an important role in modelling of problems. By using these operational matrices together, a differentialalgebraic equation can be transformed to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the techniquehttp://ijmex.com/index.php/ijmex/article/view/196/118 |
| spellingShingle | M. Heydari G. Barid Loghmani S. M. Hosseini S. M. Karbassi Direct Method to Solve Differential-Algebraic Equations by Using the Operational Matrices of Chebyshev Cardinal Functions Journal of Mathematical Extension |
| title | Direct Method to Solve Differential-Algebraic Equations by Using the Operational Matrices of Chebyshev Cardinal Functions |
| title_full | Direct Method to Solve Differential-Algebraic Equations by Using the Operational Matrices of Chebyshev Cardinal Functions |
| title_fullStr | Direct Method to Solve Differential-Algebraic Equations by Using the Operational Matrices of Chebyshev Cardinal Functions |
| title_full_unstemmed | Direct Method to Solve Differential-Algebraic Equations by Using the Operational Matrices of Chebyshev Cardinal Functions |
| title_short | Direct Method to Solve Differential-Algebraic Equations by Using the Operational Matrices of Chebyshev Cardinal Functions |
| title_sort | direct method to solve differential algebraic equations by using the operational matrices of chebyshev cardinal functions |
| url | http://ijmex.com/index.php/ijmex/article/view/196/118 |
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