Comparison of the Solution of the Van der Pol Equation Using the Modified Adomian Decomposition Method and Truncated Taylor Series Method
In this paper, we compare the solution of the van der Pol equation obtained by using the truncated Taylor series method and the modified Adomian decomposition method with the solution obtained by the Poincare-Lindstedt (P-L) method. The approximating 4-component modified Adomian decomposition method...
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| Format: | Article |
| Language: | English |
| Published: |
Nigerian Society of Physical Sciences
2020-05-01
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| Series: | Journal of Nigerian Society of Physical Sciences |
| Subjects: | |
| Online Access: | https://journal.nsps.org.ng/index.php/jnsps/article/view/44 |
| _version_ | 1818760371054313472 |
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| author | Joel Ndam O. Adedire |
| author_facet | Joel Ndam O. Adedire |
| author_sort | Joel Ndam |
| collection | DOAJ |
| description | In this paper, we compare the solution of the van der Pol equation obtained by using the truncated Taylor series method and the modified Adomian decomposition method with the solution obtained by the Poincare-Lindstedt (P-L) method. The approximating 4-component modified Adomian decomposition method behaves more like an approximate P-L analytic method than the tenth-order Taylor series. Also, with the addition of just one term, the approximating 5-component modified Adomian decomposition method produces a more convergent solution to that of P-L analytic method than the twenty second-order Taylor series approximation as the independent variable t representing time progressively increases. A general comparison of the two solutions revealed that the absolute errors generated by the approximating polynomial from the Taylor series are greater than the ones generated from the modified Adomian decomposition method. It was further revealed that very few components of the modified Adomian decomposition could yield a series of about 3 times the order of the one obtained by using the Taylor series method. Hence, we recommend the inclusion of the modified Adomian Decomposition Method in modern mathematical tools. |
| first_indexed | 2024-12-18T06:57:33Z |
| format | Article |
| id | doaj.art-ca5358aa670d4fd6898134705c1e0b4f |
| institution | Directory Open Access Journal |
| issn | 2714-2817 2714-4704 |
| language | English |
| last_indexed | 2024-12-18T06:57:33Z |
| publishDate | 2020-05-01 |
| publisher | Nigerian Society of Physical Sciences |
| record_format | Article |
| series | Journal of Nigerian Society of Physical Sciences |
| spelling | doaj.art-ca5358aa670d4fd6898134705c1e0b4f2022-12-21T21:17:09ZengNigerian Society of Physical SciencesJournal of Nigerian Society of Physical Sciences2714-28172714-47042020-05-012210.46481/jnsps.2020.44Comparison of the Solution of the Van der Pol Equation Using the Modified Adomian Decomposition Method and Truncated Taylor Series MethodJoel Ndam0O. Adedire1Department of Mathematics, University of Jos, NigeriaFederal College of Forestry, Jos, NigeriaIn this paper, we compare the solution of the van der Pol equation obtained by using the truncated Taylor series method and the modified Adomian decomposition method with the solution obtained by the Poincare-Lindstedt (P-L) method. The approximating 4-component modified Adomian decomposition method behaves more like an approximate P-L analytic method than the tenth-order Taylor series. Also, with the addition of just one term, the approximating 5-component modified Adomian decomposition method produces a more convergent solution to that of P-L analytic method than the twenty second-order Taylor series approximation as the independent variable t representing time progressively increases. A general comparison of the two solutions revealed that the absolute errors generated by the approximating polynomial from the Taylor series are greater than the ones generated from the modified Adomian decomposition method. It was further revealed that very few components of the modified Adomian decomposition could yield a series of about 3 times the order of the one obtained by using the Taylor series method. Hence, we recommend the inclusion of the modified Adomian Decomposition Method in modern mathematical tools.https://journal.nsps.org.ng/index.php/jnsps/article/view/44van der Pol oscillatormodified Adomian decomposition methodTaylor series method |
| spellingShingle | Joel Ndam O. Adedire Comparison of the Solution of the Van der Pol Equation Using the Modified Adomian Decomposition Method and Truncated Taylor Series Method Journal of Nigerian Society of Physical Sciences van der Pol oscillator modified Adomian decomposition method Taylor series method |
| title | Comparison of the Solution of the Van der Pol Equation Using the Modified Adomian Decomposition Method and Truncated Taylor Series Method |
| title_full | Comparison of the Solution of the Van der Pol Equation Using the Modified Adomian Decomposition Method and Truncated Taylor Series Method |
| title_fullStr | Comparison of the Solution of the Van der Pol Equation Using the Modified Adomian Decomposition Method and Truncated Taylor Series Method |
| title_full_unstemmed | Comparison of the Solution of the Van der Pol Equation Using the Modified Adomian Decomposition Method and Truncated Taylor Series Method |
| title_short | Comparison of the Solution of the Van der Pol Equation Using the Modified Adomian Decomposition Method and Truncated Taylor Series Method |
| title_sort | comparison of the solution of the van der pol equation using the modified adomian decomposition method and truncated taylor series method |
| topic | van der Pol oscillator modified Adomian decomposition method Taylor series method |
| url | https://journal.nsps.org.ng/index.php/jnsps/article/view/44 |
| work_keys_str_mv | AT joelndam comparisonofthesolutionofthevanderpolequationusingthemodifiedadomiandecompositionmethodandtruncatedtaylorseriesmethod AT oadedire comparisonofthesolutionofthevanderpolequationusingthemodifiedadomiandecompositionmethodandtruncatedtaylorseriesmethod |