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

Author

Listed:
  • 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
    Institute of Atomic Physics, Magurele, 077125 Bucharest, Romania)

  • Mahmoud Abdel-Ghany Nassar

    (Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo 11884, Egypt)

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.

Suggested Citation

  • Mohamed Abdel-Latif Ramadan & Dumitru Baleanu & Mahmoud Abdel-Ghany Nassar, 2019. "Highly Accurate Numerical Technique for Population Models via Rational Chebyshev Collocation Method," Mathematics, MDPI, vol. 7(10), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:913-:d:272718
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