An Efficient Numerical Scheme for Solving A Competitive Lotka-Volterra System with Two Discrete Delays

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University, Muğla, Turkey.

2 Elementary Mathematics Education Program, Faculty of Education, Muğla Sıtkı Koçman University, Muğla, Turkey.

Abstract

In this study, the Euler series solution method is developed to solve the Lotka–Volterra predator-prey model with two discrete delays. The improved method depends on a matrix-collocation method and Euler polynomials. While creating the method, all terms in the system are converted into matrix
forms. Hence the fundamental matrix equation of the system is obtained. A nonlinear algebraic
equation system is achieved by inserting the collocation points into the fundamental system. Then, the unknown coefficients that arise from Euler series expansion are calculated by solving the final system. Two different error estimation procedures are used to estimate the error of the approximation; the first one is the residual correction procedure and the second one is a technique similar to RK45. In numerical examples, the variations in the population of both species are presented by figures regarding time. Also, the method’s validity is checked by using residual error analysis.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 27 October 2024

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History

  • Receive Date: 31 January 2023
  • Revise Date: 19 October 2024
  • Accept Date: 24 October 2024

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