Abstract
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.
Highlights
Evolutionary game dynamics is a fast developing field, with applications in biology, economics, sociology, politics, interpersonal relationships, and anthropology
Analogous models for population dynamics based on the replicator equation with continuous strategy space were investigated in [9,10,11,12,13]
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]
Summary
Evolutionary game dynamics is a fast developing field, with applications in biology, economics, sociology, politics, interpersonal relationships, and anthropology. In the present paper we consider a continuous mixed strategies model for population dynamics based on an integrodifferential representation. 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].
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