Approximate analytical solutions of nonlinear Korteweg-de vries equations using multistep modified reduced differential transform method
This paper aims to propose and investigate the application of Multistep Modified Reduced Differential Transform Method (MMRDTM) for solving the nonlinear Korteweg-de Vries (KdV) equation. The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Horizon Research Publishing
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/87920/1/ABSTRACT.pdf |
| _version_ | 1796981904328622080 |
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| author | Che Hussin, Che Haziqah Md Ismail, Ahmad Izani Kilicman, Adem Azmi, Amirah |
| author_facet | Che Hussin, Che Haziqah Md Ismail, Ahmad Izani Kilicman, Adem Azmi, Amirah |
| author_sort | Che Hussin, Che Haziqah |
| collection | UPM |
| description | This paper aims to propose and investigate the application of Multistep Modified Reduced Differential Transform Method (MMRDTM) for solving the nonlinear Korteweg-de Vries (KdV) equation. The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence with a reduced number of calculated terms. MMRDTM is presented with some modification of the reduced differential transformation method (RDTM) which is the nonlinear term is replaced by related Adomian polynomials and then adopting a multistep approach. Consequently, the obtained approximation results do not only involve smaller number of calculated terms for the nonlinear KdV equation, but also converge rapidly in a broad time frame. We provided three examples to illustrates the advantages of the proposed method in obtaining the approximation solutions of the KdV equation. To depict the solution and show the validity and precision of the MMRDTM, graphical inputs are included. |
| first_indexed | 2024-03-06T10:44:28Z |
| format | Article |
| id | upm.eprints-87920 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:44:28Z |
| publishDate | 2020 |
| publisher | Horizon Research Publishing |
| record_format | dspace |
| spelling | upm.eprints-879202022-05-27T22:58:43Z http://psasir.upm.edu.my/id/eprint/87920/ Approximate analytical solutions of nonlinear Korteweg-de vries equations using multistep modified reduced differential transform method Che Hussin, Che Haziqah Md Ismail, Ahmad Izani Kilicman, Adem Azmi, Amirah This paper aims to propose and investigate the application of Multistep Modified Reduced Differential Transform Method (MMRDTM) for solving the nonlinear Korteweg-de Vries (KdV) equation. The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence with a reduced number of calculated terms. MMRDTM is presented with some modification of the reduced differential transformation method (RDTM) which is the nonlinear term is replaced by related Adomian polynomials and then adopting a multistep approach. Consequently, the obtained approximation results do not only involve smaller number of calculated terms for the nonlinear KdV equation, but also converge rapidly in a broad time frame. We provided three examples to illustrates the advantages of the proposed method in obtaining the approximation solutions of the KdV equation. To depict the solution and show the validity and precision of the MMRDTM, graphical inputs are included. Horizon Research Publishing 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/87920/1/ABSTRACT.pdf Che Hussin, Che Haziqah and Md Ismail, Ahmad Izani and Kilicman, Adem and Azmi, Amirah (2020) Approximate analytical solutions of nonlinear Korteweg-de vries equations using multistep modified reduced differential transform method. Mathematics and Statistics, 8 (2 (A)). pp. 9-16. ISSN 2332-2071; ESSN: 2332-2144 https://www.hrpub.org/journals/article_info.php?aid=8935 10.13189/ms.2020.081302 |
| spellingShingle | Che Hussin, Che Haziqah Md Ismail, Ahmad Izani Kilicman, Adem Azmi, Amirah Approximate analytical solutions of nonlinear Korteweg-de vries equations using multistep modified reduced differential transform method |
| title | Approximate analytical solutions of nonlinear Korteweg-de vries equations using multistep modified reduced differential transform method |
| title_full | Approximate analytical solutions of nonlinear Korteweg-de vries equations using multistep modified reduced differential transform method |
| title_fullStr | Approximate analytical solutions of nonlinear Korteweg-de vries equations using multistep modified reduced differential transform method |
| title_full_unstemmed | Approximate analytical solutions of nonlinear Korteweg-de vries equations using multistep modified reduced differential transform method |
| title_short | Approximate analytical solutions of nonlinear Korteweg-de vries equations using multistep modified reduced differential transform method |
| title_sort | approximate analytical solutions of nonlinear korteweg de vries equations using multistep modified reduced differential transform method |
| url | http://psasir.upm.edu.my/id/eprint/87920/1/ABSTRACT.pdf |
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