New predictor-corrector scheme for solving nonlinear differential equations with Caputo-Fabrizio operator
In this paper, we develop a new, simple, and accurate scheme to obtain approximate solution for nonlinear differential equation in the sense of Caputo-Fabrizio operator. To derive this new predictor-corrector scheme, which suits on Caputo-Fabrizio operator, firstly, we obtain the corresponding initi...
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| Format: | Article |
| Language: | en |
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Wiley Online Library
2018
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| Online Access: | http://eprints.uthm.edu.my/5899/1/AJ%202018%20%28931%29%20New%20predictor-corrector%20scheme%20for%20solving%20nonlinear%20differential%20equations%20with%20Caputo-Fabrizio%20operator.pdf http://eprints.uthm.edu.my/5899/ |
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| author | Teng, Toh Yoke Phang, Chang Rong, Loh Jian |
| author_facet | Teng, Toh Yoke Phang, Chang Rong, Loh Jian |
| author_sort | Teng, Toh Yoke |
| building | UTHM Library |
| collection | Institutional Repository |
| content_provider | Universiti Tun Hussein Onn Malaysia |
| content_source | UTHM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | In this paper, we develop a new, simple, and accurate scheme to obtain approximate solution for nonlinear differential equation in the sense of Caputo-Fabrizio operator. To derive this new predictor-corrector scheme, which suits on Caputo-Fabrizio operator, firstly, we obtain the corresponding initial value problem for the differential equation in the Caputo-Fabrizio sense. Hence, by fractional Euler method and fractional trapeziodal rule, we obtain the predictor formula as well as corrector formula. Error analysis for this new method is derived. To test the validity and simplicity of this method, some illustrative examples for nonlinear differential equations are solved. |
| format | Article |
| id | my.uthm.eprints-5899 |
| institution | Universiti Tun Hussein Onn Malaysia |
| language | en |
| publishDate | 2018 |
| publisher | Wiley Online Library |
| record_format | eprints |
| spelling | my.uthm.eprints-58992022-01-24T07:59:40Z http://eprints.uthm.edu.my/5899/ New predictor-corrector scheme for solving nonlinear differential equations with Caputo-Fabrizio operator Teng, Toh Yoke Phang, Chang Rong, Loh Jian T57-57.97 Applied mathematics. Quantitative methods In this paper, we develop a new, simple, and accurate scheme to obtain approximate solution for nonlinear differential equation in the sense of Caputo-Fabrizio operator. To derive this new predictor-corrector scheme, which suits on Caputo-Fabrizio operator, firstly, we obtain the corresponding initial value problem for the differential equation in the Caputo-Fabrizio sense. Hence, by fractional Euler method and fractional trapeziodal rule, we obtain the predictor formula as well as corrector formula. Error analysis for this new method is derived. To test the validity and simplicity of this method, some illustrative examples for nonlinear differential equations are solved. Wiley Online Library 2018 Article PeerReviewed text en http://eprints.uthm.edu.my/5899/1/AJ%202018%20%28931%29%20New%20predictor-corrector%20scheme%20for%20solving%20nonlinear%20differential%20equations%20with%20Caputo-Fabrizio%20operator.pdf Teng, Toh Yoke and Phang, Chang and Rong, Loh Jian (2018) New predictor-corrector scheme for solving nonlinear differential equations with Caputo-Fabrizio operator. Mathematical Methods in the Applied Sciences, 42 (1). pp. 175-185. ISSN 1099-1476 |
| spellingShingle | T57-57.97 Applied mathematics. Quantitative methods Teng, Toh Yoke Phang, Chang Rong, Loh Jian New predictor-corrector scheme for solving nonlinear differential equations with Caputo-Fabrizio operator |
| title | New predictor-corrector scheme for solving nonlinear differential equations with Caputo-Fabrizio operator |
| title_full | New predictor-corrector scheme for solving nonlinear differential equations with Caputo-Fabrizio operator |
| title_fullStr | New predictor-corrector scheme for solving nonlinear differential equations with Caputo-Fabrizio operator |
| title_full_unstemmed | New predictor-corrector scheme for solving nonlinear differential equations with Caputo-Fabrizio operator |
| title_short | New predictor-corrector scheme for solving nonlinear differential equations with Caputo-Fabrizio operator |
| title_sort | new predictor-corrector scheme for solving nonlinear differential equations with caputo-fabrizio operator |
| topic | T57-57.97 Applied mathematics. Quantitative methods |
| url | http://eprints.uthm.edu.my/5899/1/AJ%202018%20%28931%29%20New%20predictor-corrector%20scheme%20for%20solving%20nonlinear%20differential%20equations%20with%20Caputo-Fabrizio%20operator.pdf http://eprints.uthm.edu.my/5899/ |
| url_provider | http://eprints.uthm.edu.my/ |