An operational matrix method to solve the Lotka–Volterra predator–prey models with discrete delays

Abstract

In this paper, we consider the Lotka–Volterra predator–prey model with discrete delays. We apply the operational matrix method in [20] to this model which corresponds to a problem of nonlinear differential equations. The method is based on the operational matrices of the standard bases functions. In order to find the polynomial approximations of the known functions in the equation, the operational matrices are created by the least-squares method. The method converts the problem into a system of algebraic equations. By solving this system, the coefficients are determined. The approximate solutions are obtained by writing the coefficients in form of the approximate solutions. In addition, the accuracy of the approximate solution is checked and an error estimation technique is presented. The method is applied to some examples and the numerical results are reported. Numerical applications and comparisons with other methods show the efficiency of the current one.