Highly Accurate Numerical Technique for Population Models via Rational Chebyshev Collocation Method

Mohamed Abdel-Latif Ramadan, Dumitru Baleanu and Mahmoud Abdel-Ghany Nassar
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Mohamed Abdel-Latif Ramadan: Mathematics & Computer Science Department, Faculty of Science, Menoufia University, Menoufia 11352, Egypt
Dumitru Baleanu: Department of Mathematics, Cankaya University, Ankara 06530, Turkey
Mahmoud Abdel-Ghany Nassar: Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo 11884, Egypt

Mathematics, 2019, vol. 7, issue 10, 1-15

Abstract: The present work introduces the application of rational Chebyshev collocation technique for approximating bio-mathematical problems of continuous population models for single and interacting species (C.P.M.). We study systematically the logistic growth model in a population, prey-predator model: Lotka-Volterra system (L.V.M.), the simple two-species Lotka-Volterra competition model (L.V.C.M.) and the prey-predator model with limit cycle periodic behavior (P.P.M.). For testing the accuracy, the numerical results for our method and others existing methods as well as the exact solution are compared. The obtained numerical results indicate the ability, the reliability and the accuracy of the present method.

Keywords: rational Chebyshev functions; continuous population models; rational Chebyshev collocation method; nonlinear differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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