A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model
A new shifted Legendre-Gauss collocation method is proposed for the solution of Volterra’s model for population growth of a species in a closed system. Volterra’s model is a nonlinear integrodifferential equation on a semi-infinite domain, where the integral term represents the effects of toxin. In...
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| Format: | Article |
| Language: | English English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30262/ http://psasir.upm.edu.my/id/eprint/30262/1/A%20multiple.pdf |
| _version_ | 1848846627244081152 |
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| author | Kajani, Majid Tavassoli Maleki, Mohammad Kilicman, Adem |
| author_facet | Kajani, Majid Tavassoli Maleki, Mohammad Kilicman, Adem |
| author_sort | Kajani, Majid Tavassoli |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A new shifted Legendre-Gauss collocation method is proposed for the solution of Volterra’s model for population growth of a species in a closed system. Volterra’s model is a nonlinear integrodifferential equation on a semi-infinite domain, where the integral term represents the effects of toxin. In this method, by choosing a step size, the original problem is replaced with a sequence of initial value problems in subintervals. The obtained initial value problems are then step by step reduced to systems of algebraic equations using collocation. The initial conditions for each step are obtained from the approximated solution at its previous step. It is shown that the accuracy can be improved by either increasing the collocation points or decreasing the step size. The method seems easy to implement and computationally attractive. Numerical findings demonstrate the applicability and high accuracy of the proposed method. |
| first_indexed | 2025-11-15T09:05:43Z |
| format | Article |
| id | upm-30262 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T09:05:43Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-302622015-09-20T23:51:29Z http://psasir.upm.edu.my/id/eprint/30262/ A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model Kajani, Majid Tavassoli Maleki, Mohammad Kilicman, Adem A new shifted Legendre-Gauss collocation method is proposed for the solution of Volterra’s model for population growth of a species in a closed system. Volterra’s model is a nonlinear integrodifferential equation on a semi-infinite domain, where the integral term represents the effects of toxin. In this method, by choosing a step size, the original problem is replaced with a sequence of initial value problems in subintervals. The obtained initial value problems are then step by step reduced to systems of algebraic equations using collocation. The initial conditions for each step are obtained from the approximated solution at its previous step. It is shown that the accuracy can be improved by either increasing the collocation points or decreasing the step size. The method seems easy to implement and computationally attractive. Numerical findings demonstrate the applicability and high accuracy of the proposed method. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30262/1/A%20multiple.pdf Kajani, Majid Tavassoli and Maleki, Mohammad and Kilicman, Adem (2013) A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model. Mathematical Problems in Engineering, 2013. art. no. 783069. pp. 1-6. ISSN 1024-123X http://www.hindawi.com/journals/mpe/2013/783069/ 10.1155/2013/783069 English |
| spellingShingle | Kajani, Majid Tavassoli Maleki, Mohammad Kilicman, Adem A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model |
| title | A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model |
| title_full | A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model |
| title_fullStr | A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model |
| title_full_unstemmed | A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model |
| title_short | A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model |
| title_sort | multiple-step legendre-gauss collocation method for solving volterra's population growth model |
| url | http://psasir.upm.edu.my/id/eprint/30262/ http://psasir.upm.edu.my/id/eprint/30262/ http://psasir.upm.edu.my/id/eprint/30262/ http://psasir.upm.edu.my/id/eprint/30262/1/A%20multiple.pdf |