Homotopy perturbation method for fractional gas dynamics equation using Sumudu transform
A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved by Adomian decomposition method (ADM). The re...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30136/1/30136.pdf |
| _version_ | 1796971680395952128 |
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| author | Singh, Jagdev Kumar, Devendra Kilicman, Adem |
| author_facet | Singh, Jagdev Kumar, Devendra Kilicman, Adem |
| author_sort | Singh, Jagdev |
| collection | UPM |
| description | A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement and hence this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive. |
| first_indexed | 2024-03-06T08:16:36Z |
| format | Article |
| id | upm.eprints-30136 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:16:36Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| record_format | dspace |
| spelling | upm.eprints-301362017-10-20T03:40:52Z http://psasir.upm.edu.my/id/eprint/30136/ Homotopy perturbation method for fractional gas dynamics equation using Sumudu transform Singh, Jagdev Kumar, Devendra Kilicman, Adem A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement and hence this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30136/1/30136.pdf Singh, Jagdev and Kumar, Devendra and Kilicman, Adem (2013) Homotopy perturbation method for fractional gas dynamics equation using Sumudu transform. Abstract and Applied Analysis, 2013. art. no. 934060. pp. 1-8. ISSN 1085-3375; ESSN: 1687-0409 http://www.hindawi.com/journals/aaa/2013/934060/ 10.1155/2013/934060 |
| spellingShingle | Singh, Jagdev Kumar, Devendra Kilicman, Adem Homotopy perturbation method for fractional gas dynamics equation using Sumudu transform |
| title | Homotopy perturbation method for fractional gas dynamics equation using Sumudu transform |
| title_full | Homotopy perturbation method for fractional gas dynamics equation using Sumudu transform |
| title_fullStr | Homotopy perturbation method for fractional gas dynamics equation using Sumudu transform |
| title_full_unstemmed | Homotopy perturbation method for fractional gas dynamics equation using Sumudu transform |
| title_short | Homotopy perturbation method for fractional gas dynamics equation using Sumudu transform |
| title_sort | homotopy perturbation method for fractional gas dynamics equation using sumudu transform |
| url | http://psasir.upm.edu.my/id/eprint/30136/1/30136.pdf |
| work_keys_str_mv | AT singhjagdev homotopyperturbationmethodforfractionalgasdynamicsequationusingsumudutransform AT kumardevendra homotopyperturbationmethodforfractionalgasdynamicsequationusingsumudutransform AT kilicmanadem homotopyperturbationmethodforfractionalgasdynamicsequationusingsumudutransform |