An efficient numerical scheme for solving a competitive Lotka-Volterra system with two discrete delays

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 the 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 RK۴۵. 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.

کلیدواژه ها:

Error estimation ، Euler series solution method ، Delayed prey-predator system