The Homotopy Perturbation Method to Solve Initial Value Problems of First Order with Discontinuities
In this work, the homotopy perturbation method (HPM) is used to solve initial valueproblems of first order with various types of discontinuities. The numerical results obtained (arecompared) using the traditional HPM, and the integral equation of the nth equation with thesolution numerical obtained...
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| Format: | Article |
| Language: | English |
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Mosul University
2022-12-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
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| Online Access: | https://csmj.mosuljournals.com/article_176592_4a46a82cd283bb44de628f777b4f38d5.pdf |
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| _version_ | 1849691431193542656 |
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| author | Mohammed Ahmed Waleed Al-Hayani |
| author_facet | Mohammed Ahmed Waleed Al-Hayani |
| author_sort | Mohammed Ahmed |
| collection | DOAJ |
| description | In this work, the homotopy perturbation method (HPM) is used to solve initial valueproblems of first order with various types of discontinuities. The numerical results obtained (arecompared) using the traditional HPM, and the integral equation of the nth equation with thesolution numerical obtained using Simpson and Trapezoidal Rules to demonstrate that thesolution results are extremely accurate when compared to the exact solution. The maximumabsolute error, ‖ . ‖ , maximum relative error, maximum residual error, and expectedconvergence order are also provided. |
| format | Article |
| id | doaj-art-e7cbbf3b37134d40a5dc146809d8c776 |
| institution | DOAJ |
| issn | 1815-4816 2311-7990 |
| language | English |
| publishDate | 2022-12-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj-art-e7cbbf3b37134d40a5dc146809d8c7762025-08-20T03:21:02ZengMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902022-12-01162617010.33899/csmj.2022.176592176592The Homotopy Perturbation Method to Solve Initial Value Problems of First Order with DiscontinuitiesMohammed AhmedWaleed Al-Hayani0College of Computer Science and Mathematics / Mosul UniversityIn this work, the homotopy perturbation method (HPM) is used to solve initial valueproblems of first order with various types of discontinuities. The numerical results obtained (arecompared) using the traditional HPM, and the integral equation of the nth equation with thesolution numerical obtained using Simpson and Trapezoidal Rules to demonstrate that thesolution results are extremely accurate when compared to the exact solution. The maximumabsolute error, ‖ . ‖ , maximum relative error, maximum residual error, and expectedconvergence order are also provided.https://csmj.mosuljournals.com/article_176592_4a46a82cd283bb44de628f777b4f38d5.pdfhomotopy perturbation methodhe’s polynomialsinitial value problems (ivps)unit step functionunit impulse functionsimpson ruletrapezoidal rule |
| spellingShingle | Mohammed Ahmed Waleed Al-Hayani The Homotopy Perturbation Method to Solve Initial Value Problems of First Order with Discontinuities Al-Rafidain Journal of Computer Sciences and Mathematics homotopy perturbation method he’s polynomials initial value problems (ivps) unit step function unit impulse function simpson rule trapezoidal rule |
| title | The Homotopy Perturbation Method to Solve Initial Value Problems of First Order with Discontinuities |
| title_full | The Homotopy Perturbation Method to Solve Initial Value Problems of First Order with Discontinuities |
| title_fullStr | The Homotopy Perturbation Method to Solve Initial Value Problems of First Order with Discontinuities |
| title_full_unstemmed | The Homotopy Perturbation Method to Solve Initial Value Problems of First Order with Discontinuities |
| title_short | The Homotopy Perturbation Method to Solve Initial Value Problems of First Order with Discontinuities |
| title_sort | homotopy perturbation method to solve initial value problems of first order with discontinuities |
| topic | homotopy perturbation method he’s polynomials initial value problems (ivps) unit step function unit impulse function simpson rule trapezoidal rule |
| url | https://csmj.mosuljournals.com/article_176592_4a46a82cd283bb44de628f777b4f38d5.pdf |
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