Pell–Lucas collocation method for numerical solutions of two population models and residual correction
Our aim in this article is to present a collocation method to solve two population models for single and interacting species. For this, logistic growth model and prey–predator model are examined. These models are solved numerically by Pell–Lucas collocation method. The method gives the approximate s...
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Online Access: | http://dx.doi.org/10.1080/16583655.2020.1816027 |
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doaj-ae91205e50e04d7a9f7fdf12974f0c902021-01-26T12:13:36ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552020-01-011411262127810.1080/16583655.2020.18160271816027Pell–Lucas collocation method for numerical solutions of two population models and residual correctionŞuayip Yüzbaşı0Gamze Yıldırım1Department of Mathematics, Faculty of Science, Akdeniz UniversityDepartment of Mathematics, Faculty of Science, Akdeniz UniversityOur aim in this article is to present a collocation method to solve two population models for single and interacting species. For this, logistic growth model and prey–predator model are examined. These models are solved numerically by Pell–Lucas collocation method. The method gives the approximate solutions of these models in form of truncated Pell–Lucas series. By utilizing Pell–Lucas collocation method, non-linear mathematical models are converted to a system of non-linear algebraic equations. This non-linear equation system is solved and the obtained coefficients are the coefficients of the truncated Pell–Lucas serie solution. Furthermore, the residual correction method is used to find better approximate solutions. All results are shown in tables and graphs for different $(N, M) $ values, and additionally the comparisons are made with other methods from. It is seen that the method gives effective results to the presented model problems.http://dx.doi.org/10.1080/16583655.2020.1816027collocation methodlogistic growth modellotka–volterra modelnon-linear differential equations and their systemspell–lucas polynomialsprey and predator model |
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DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Şuayip Yüzbaşı Gamze Yıldırım |
spellingShingle |
Şuayip Yüzbaşı Gamze Yıldırım Pell–Lucas collocation method for numerical solutions of two population models and residual correction Journal of Taibah University for Science collocation method logistic growth model lotka–volterra model non-linear differential equations and their systems pell–lucas polynomials prey and predator model |
author_facet |
Şuayip Yüzbaşı Gamze Yıldırım |
author_sort |
Şuayip Yüzbaşı |
title |
Pell–Lucas collocation method for numerical solutions of two population models and residual correction |
title_short |
Pell–Lucas collocation method for numerical solutions of two population models and residual correction |
title_full |
Pell–Lucas collocation method for numerical solutions of two population models and residual correction |
title_fullStr |
Pell–Lucas collocation method for numerical solutions of two population models and residual correction |
title_full_unstemmed |
Pell–Lucas collocation method for numerical solutions of two population models and residual correction |
title_sort |
pell–lucas collocation method for numerical solutions of two population models and residual correction |
publisher |
Taylor & Francis Group |
series |
Journal of Taibah University for Science |
issn |
1658-3655 |
publishDate |
2020-01-01 |
description |
Our aim in this article is to present a collocation method to solve two population models for single and interacting species. For this, logistic growth model and prey–predator model are examined. These models are solved numerically by Pell–Lucas collocation method. The method gives the approximate solutions of these models in form of truncated Pell–Lucas series. By utilizing Pell–Lucas collocation method, non-linear mathematical models are converted to a system of non-linear algebraic equations. This non-linear equation system is solved and the obtained coefficients are the coefficients of the truncated Pell–Lucas serie solution. Furthermore, the residual correction method is used to find better approximate solutions. All results are shown in tables and graphs for different $(N, M) $ values, and additionally the comparisons are made with other methods from. It is seen that the method gives effective results to the presented model problems. |
topic |
collocation method logistic growth model lotka–volterra model non-linear differential equations and their systems pell–lucas polynomials prey and predator model |
url |
http://dx.doi.org/10.1080/16583655.2020.1816027 |
work_keys_str_mv |
AT suayipyuzbası pelllucascollocationmethodfornumericalsolutionsoftwopopulationmodelsandresidualcorrection AT gamzeyıldırım pelllucascollocationmethodfornumericalsolutionsoftwopopulationmodelsandresidualcorrection |
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1724322678846783488 |