The Derivation of Convergence Analysis for the Multistage Adomian Decomposition Method for solving the Autonomous Van der Pol system
Abstract<br /> The autonomous Van der Pol system was solved accurately by MADM [4]. The method has the advantage of giving the form of the numerical solution within each time interval which is not possible in purely numerical techniques like RK45 and classical ADM. In this paper we will derive...
| Main Authors: | , , |
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| Format: | Article |
| Language: | Arabic |
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College of Education for Pure Sciences
1999-11-01
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| Series: | مجلة التربية والعلم |
| Subjects: | |
| Online Access: | https://edusj.mosuljournals.com/article_58798_79d4b564a92fb14b57acbf172e215791.pdf |
| _version_ | 1828764799147704320 |
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| author | Abbas AL-Bayati Ann Al-Sawoor Merna Samarji |
| author_facet | Abbas AL-Bayati Ann Al-Sawoor Merna Samarji |
| author_sort | Abbas AL-Bayati |
| collection | DOAJ |
| description | Abstract<br /> The autonomous Van der Pol system was solved accurately by MADM [4]. The method has the advantage of giving the form of the numerical solution within each time interval which is not possible in purely numerical techniques like RK45 and classical ADM. In this paper we will derive the convergence of A Multistage Adomian Decomposition Method (MADM) by deriving the Homotopy Analysis Method for this system. We will show that if the series<br /> <br /> where <br /> <br /> is convergent and it must be a solution of Van der Pol system, then the two sequences are converges to zero. |
| first_indexed | 2024-12-11T06:37:49Z |
| format | Article |
| id | doaj.art-6888792f11b244dbb03b39c667b66111 |
| institution | Directory Open Access Journal |
| issn | 1812-125X 2664-2530 |
| language | Arabic |
| last_indexed | 2024-12-11T06:37:49Z |
| publishDate | 1999-11-01 |
| publisher | College of Education for Pure Sciences |
| record_format | Article |
| series | مجلة التربية والعلم |
| spelling | doaj.art-6888792f11b244dbb03b39c667b661112022-12-22T01:17:19ZaraCollege of Education for Pure Sciencesمجلة التربية والعلم1812-125X2664-25301999-11-0124313314810.33899/edusj.1999.5879858798The Derivation of Convergence Analysis for the Multistage Adomian Decomposition Method for solving the Autonomous Van der Pol systemAbbas AL-Bayati0Ann Al-Sawoor1Merna Samarji2Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, IraqDepartment of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, IraqDepartment of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, IraqAbstract<br /> The autonomous Van der Pol system was solved accurately by MADM [4]. The method has the advantage of giving the form of the numerical solution within each time interval which is not possible in purely numerical techniques like RK45 and classical ADM. In this paper we will derive the convergence of A Multistage Adomian Decomposition Method (MADM) by deriving the Homotopy Analysis Method for this system. We will show that if the series<br /> <br /> where <br /> <br /> is convergent and it must be a solution of Van der Pol system, then the two sequences are converges to zero.https://edusj.mosuljournals.com/article_58798_79d4b564a92fb14b57acbf172e215791.pdfconvergence analysismultistage adomian decomposition methodautonomous van der pol system |
| spellingShingle | Abbas AL-Bayati Ann Al-Sawoor Merna Samarji The Derivation of Convergence Analysis for the Multistage Adomian Decomposition Method for solving the Autonomous Van der Pol system مجلة التربية والعلم convergence analysis multistage adomian decomposition method autonomous van der pol system |
| title | The Derivation of Convergence Analysis for the Multistage Adomian Decomposition Method for solving the Autonomous Van der Pol system |
| title_full | The Derivation of Convergence Analysis for the Multistage Adomian Decomposition Method for solving the Autonomous Van der Pol system |
| title_fullStr | The Derivation of Convergence Analysis for the Multistage Adomian Decomposition Method for solving the Autonomous Van der Pol system |
| title_full_unstemmed | The Derivation of Convergence Analysis for the Multistage Adomian Decomposition Method for solving the Autonomous Van der Pol system |
| title_short | The Derivation of Convergence Analysis for the Multistage Adomian Decomposition Method for solving the Autonomous Van der Pol system |
| title_sort | derivation of convergence analysis for the multistage adomian decomposition method for solving the autonomous van der pol system |
| topic | convergence analysis multistage adomian decomposition method autonomous van der pol system |
| url | https://edusj.mosuljournals.com/article_58798_79d4b564a92fb14b57acbf172e215791.pdf |
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