Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations
The main aim of this work is to present a user friendly numerical algorithm based on homotopy perturbation Sumudu transform method for nonlinear fractional partial differential arising in spatial diffusion of biological populations in animals. The movements are made generally either by mature animal...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/535793 |
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| author | Jagdev Singh Devendra Kumar Adem Kılıçman |
| author_facet | Jagdev Singh Devendra Kumar Adem Kılıçman |
| author_sort | Jagdev Singh |
| collection | DOAJ |
| description | The main aim of this work is to present a user friendly numerical algorithm based on homotopy perturbation Sumudu transform method for nonlinear fractional partial differential arising in spatial diffusion of biological populations in animals. The movements are made generally either by mature animals driven out by invaders or by young animals just reaching maturity moving out of their parental territory to establish breeding territory of their own. The homotopy perturbation Sumudu transform method is a combined form of the Sumudu transform method and homotopy perturbation method. The obtained results are compared with Sumudu decomposition method. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and accurate. These results reveal that the proposed method is computationally very attractive. |
| format | Article |
| id | doaj-art-42a07adc84f645e193802dcf7fe36631 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-42a07adc84f645e193802dcf7fe366312025-02-03T05:46:25ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/535793535793Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological PopulationsJagdev Singh0Devendra Kumar1Adem Kılıçman2Department of Mathematics, Jagannath University, Jaipur-303901, Rajasthan, IndiaDepartment of Mathematics, Jagannath Gupta Institute of Engineering and Technology, Jaipur-302022, Rajasthan, IndiaDepartment of Mathematics and Institute for Mathematical Research University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaThe main aim of this work is to present a user friendly numerical algorithm based on homotopy perturbation Sumudu transform method for nonlinear fractional partial differential arising in spatial diffusion of biological populations in animals. The movements are made generally either by mature animals driven out by invaders or by young animals just reaching maturity moving out of their parental territory to establish breeding territory of their own. The homotopy perturbation Sumudu transform method is a combined form of the Sumudu transform method and homotopy perturbation method. The obtained results are compared with Sumudu decomposition method. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and accurate. These results reveal that the proposed method is computationally very attractive.http://dx.doi.org/10.1155/2014/535793 |
| spellingShingle | Jagdev Singh Devendra Kumar Adem Kılıçman Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations Abstract and Applied Analysis |
| title | Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations |
| title_full | Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations |
| title_fullStr | Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations |
| title_full_unstemmed | Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations |
| title_short | Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations |
| title_sort | numerical solutions of nonlinear fractional partial differential equations arising in spatial diffusion of biological populations |
| url | http://dx.doi.org/10.1155/2014/535793 |
| work_keys_str_mv | AT jagdevsingh numericalsolutionsofnonlinearfractionalpartialdifferentialequationsarisinginspatialdiffusionofbiologicalpopulations AT devendrakumar numericalsolutionsofnonlinearfractionalpartialdifferentialequationsarisinginspatialdiffusionofbiologicalpopulations AT ademkılıcman numericalsolutionsofnonlinearfractionalpartialdifferentialequationsarisinginspatialdiffusionofbiologicalpopulations |