Operational matrix based on Genocchi polynomials for solution of delay differential equations
In this paper, we present a new simple and effective algorithm for solving generalized Pantograph equa-tions, delay differential equations with neutral terms and delay differential system with constant and variable coefficients.The new method is based on one of the Appell polynomials, namely Genocchi...
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| Format: | Article |
| Language: | English |
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Elsevier Ltd
2017
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| Online Access: | http://eprints.uthm.edu.my/5197/1/AJ%202017%20%28330%29%20Operational%20matrix%20based%20on%20Genocchi%20polynomials.pdf |
| _version_ | 1825709983042371584 |
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| author | Isah, Abdulnasir Phang, Chang |
| author_facet | Isah, Abdulnasir Phang, Chang |
| author_sort | Isah, Abdulnasir |
| collection | UTHM |
| description | In this paper, we present a new simple and effective algorithm for solving generalized Pantograph equa-tions, delay differential equations with neutral terms and delay differential system with constant and variable coefficients.The new method is based on one of the Appell polynomials, namely Genocchi poly-nomials. We first introduce the properties of Genocchi polynomials and employed them to construct the operational matrices of derivative. Collocation method based on this operational matrix is used. Error estimate for this scheme based on the Generalized pantograph equations is reproduced. Only few terms of Genocchi polynomials are needed to obtain very good results. Numerical examples with comparison show the simplicity, efficiency and accuracy of the method. |
| first_indexed | 2024-03-05T21:50:41Z |
| format | Article |
| id | uthm.eprints-5197 |
| institution | Universiti Tun Hussein Onn Malaysia |
| language | English |
| last_indexed | 2024-03-05T21:50:41Z |
| publishDate | 2017 |
| publisher | Elsevier Ltd |
| record_format | dspace |
| spelling | uthm.eprints-51972022-01-06T04:23:11Z http://eprints.uthm.edu.my/5197/ Operational matrix based on Genocchi polynomials for solution of delay differential equations Isah, Abdulnasir Phang, Chang HA Statistics QA273-280 Probabilities. Mathematical statistics In this paper, we present a new simple and effective algorithm for solving generalized Pantograph equa-tions, delay differential equations with neutral terms and delay differential system with constant and variable coefficients.The new method is based on one of the Appell polynomials, namely Genocchi poly-nomials. We first introduce the properties of Genocchi polynomials and employed them to construct the operational matrices of derivative. Collocation method based on this operational matrix is used. Error estimate for this scheme based on the Generalized pantograph equations is reproduced. Only few terms of Genocchi polynomials are needed to obtain very good results. Numerical examples with comparison show the simplicity, efficiency and accuracy of the method. Elsevier Ltd 2017 Article PeerReviewed text en http://eprints.uthm.edu.my/5197/1/AJ%202017%20%28330%29%20Operational%20matrix%20based%20on%20Genocchi%20polynomials.pdf Isah, Abdulnasir and Phang, Chang (2017) Operational matrix based on Genocchi polynomials for solution of delay differential equations. Ain Shams Engineering. pp. 1-6. ISSN 2090-4479 http://dx.doi.org/10.1016/j.asej.2016.09.015 |
| spellingShingle | HA Statistics QA273-280 Probabilities. Mathematical statistics Isah, Abdulnasir Phang, Chang Operational matrix based on Genocchi polynomials for solution of delay differential equations |
| title | Operational matrix based on Genocchi polynomials for solution of delay differential equations |
| title_full | Operational matrix based on Genocchi polynomials for solution of delay differential equations |
| title_fullStr | Operational matrix based on Genocchi polynomials for solution of delay differential equations |
| title_full_unstemmed | Operational matrix based on Genocchi polynomials for solution of delay differential equations |
| title_short | Operational matrix based on Genocchi polynomials for solution of delay differential equations |
| title_sort | operational matrix based on genocchi polynomials for solution of delay differential equations |
| topic | HA Statistics QA273-280 Probabilities. Mathematical statistics |
| url | http://eprints.uthm.edu.my/5197/1/AJ%202017%20%28330%29%20Operational%20matrix%20based%20on%20Genocchi%20polynomials.pdf |
| work_keys_str_mv | AT isahabdulnasir operationalmatrixbasedongenocchipolynomialsforsolutionofdelaydifferentialequations AT phangchang operationalmatrixbasedongenocchipolynomialsforsolutionofdelaydifferentialequations |