Sinc Collocation Method for Finding Numerical Solution of Integrodifferential Model Arisen in Continuous Mixed Strategy

One of the new techniques is used to solve numerical problems involving integral equations and ordinary differential equations known as Sinc collocation methods. This method has been shown to be an efficient numerical tool for finding solution. The construction mixed strategies evolutionary game can be transformed to an integrodifferential problem. Properties of the sinc procedure are utilized to reduce the computation of this integrodifferential to some algebraic equations. The method is applied to a few test examples to illustrate the accuracy and implementation of the method. 1. Introduction Evolutionary game dynamics is a fast developing field, with applications in biology, economics, sociology, politics, interpersonal relationships, and anthropology. Background material and countless references can be found in [1–8]. In the present paper we consider a continuous mixed strategies model for population dynamics based on an integrodifferential representation. Analogous models for population dynamics based on the replicator equation with continuous strategy space were investigated in [9–13]. For the moment based model has proved global existence of solutions and studied the asymptotic behavior and stability of solutions in the case of two strategies [14]. In the last three decades a variety of numerical methods based on the sinc approximation have been developed. Sinc methods were developed by Stenger [15] and Lund and Bowers [16] and it is widely used for solving a wide range of linear and nonlinear problems arising from scientific and engineering applications including oceanographic problems with boundary layers [17], two-point boundary value problems [18], astrophysics equations [19], Blasius equation [20], Volterras population model [21], Hallens integral equation [22], third-order boundary value problems [23], system of second-order boundary value problems [24], fourth-order boundary value problems [25], heat distribution [26], elastoplastic problem [27], inverse problem [28, 29], integrodifferential equation [30], optimal control [15], nonlinear boundary-value problems [31], and multipoint boundary value problems [32]. Very recently authors of [33] used the sinc procedure to solve linear and nonlinear Volterra integral and integrodifferential equations. The content of this paper is arranged in seven sections. In Section 2, I discuss the modeling of the problem in an integrodifferential form. Section 3, introduces some general concepts concerning the sinc approximation. Section 4, contains some preliminaries in collocation method. In Section 5, the