Approximating Ordinary Differential Equations by Means of the Chess Game Moves  

作　　者：Maria Teresa Signes-Pont Joan Boters-Pitarch José Juan Cortés-Plana Higinio Mora-Mora Maria Teresa Signes-Pont;Joan Boters-Pitarch;José Juan Cortés-Plana;Higinio Mora-Mora(Department of Computer Science and Technology, University of Alicante, Alicante, Spain)

机构地区：[1]Department of Computer Science and Technology, University of Alicante, Alicante, Spain

出　　处：《Journal of Applied Mathematics and Physics》2022年第10期3240-3263,共24页应用数学与应用物理（英文）

摘　　要：The chess game provides a very rich experience in neighborhood types. The chess pieces have vertical, horizontal, diagonal, up/down or combined movements on one or many squares of the chess. These movements can associate with neighborhoods. Our work aims to set a behavioral approximation between calculations carried out by means of traditional computation tools such as ordinary differential equations (ODEs) and the evolution of the value of the cells caused by the chess game moves. Our proposal is based on a grid. The cells’ value changes as time pass depending on both their neighborhood and an update rule. This framework succeeds in applying real data matching in the cases of the ODEs used in compartmental models of disease expansion, such as the well-known Susceptible-Infected Recovered (SIR) model and its derivatives, as well as in the case of population dynamics in competition for resources, depicted by the Lotke-Volterra model.The chess game provides a very rich experience in neighborhood types. The chess pieces have vertical, horizontal, diagonal, up/down or combined movements on one or many squares of the chess. These movements can associate with neighborhoods. Our work aims to set a behavioral approximation between calculations carried out by means of traditional computation tools such as ordinary differential equations (ODEs) and the evolution of the value of the cells caused by the chess game moves. Our proposal is based on a grid. The cells’ value changes as time pass depending on both their neighborhood and an update rule. This framework succeeds in applying real data matching in the cases of the ODEs used in compartmental models of disease expansion, such as the well-known Susceptible-Infected Recovered (SIR) model and its derivatives, as well as in the case of population dynamics in competition for resources, depicted by the Lotke-Volterra model.

关 键 词：Chess Game NEIGHBORHOOD Update Rule ODE SIR Model Lotke-Volterra Model 

分 类 号：O17[理学—数学]