Accurate and efficient matrix techniques for solving the fractional Lotka–Volterra population model

Mohammad Izadi, Şuayip Yüzbaşı and Waleed Adel

Physica A: Statistical Mechanics and its Applications, 2022, vol. 600, issue C

Abstract: This paper aims to develop accurate novel collocation techniques for solving a fractional fractional-order Lotka–Volterra (LV) predator–prey model. This type of equation has a wide variety of applications in biology to simulate the interaction between two different species. The fractional-order operator is defined in the Caputo sense. We introduce some new polynomials for solving this type of equation named the Morgan-Voyce polynomials. These new techniques named direct and quasilinear Morgan-Voyce techniques are presented and then used to solve the LV system revealing some of the new features of the model. Some of the advantages of the application of these techniques are that they are straightforward along with high accuracy. Detailed error and convergence analysis for the proposed methods are provided revealing the upper bound for these techniques. To test the accuracy of the proposed methods, the methods are tested on several examples with different values of the parameters and fractional orders and also compared with each other and with other related methods from the literature. The results are demonstrated through tables and figures and conclude that the provided technique is highly accurate compared to the other methods. The results revealed the agreement between the obtained approximate solution and the dynamics of the described model. These methods can be considered as promising to adapt to other similar models with application to different areas of engineering and biology.

Keywords: Collocation points; Error and convergence analysis; Fractional-order predator–prey model; Caputo’s fractional derivative; Morgan-Voyce polynomials; Quasilinearization method (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:600:y:2022:i:c:s0378437122003879

DOI: 10.1016/j.physa.2022.127558

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