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Author Gonzalez, E.; Villena, M.J. pdf  doi
  Title Spatial attrition modeling: Stability conditions for a 2D + t FD formulation Type
  Year 2011 Publication Computers & Mathematics With Applications Abbreviated Journal Comput. Math. Appl.  
  Volume 61 Issue 11 Pages 3246-3257  
  Keywords PDE; Stability; Reaction-diffusion; Spatial attrition modeling  
  Abstract A new general formulation for the spatial modeling of combat is presented, where the main drivers are movement attitudes and struggle evolution. This model in its simplest form is represented by a linear set of two coupled partial differential equations for two independent functions of the space and time variables. Even though the problem has a linear shape, non-negative values for the two functions render this problem as nonlinear. In contrast with other attempts, this model ensures stability and theoretical consistency with the original Lanchester Equations, allowing for a better understanding and interpretation of the spatial modeling. As a numerical illustration a simple combat situation is developed. The model is calibrated to simulate different troop movement tactics that allow an invader force to provoke maximum damage at a minimum cost. The analysis provided here reviews the trade-off between spatial grid and time stepping for attrition cases and then extends it to a new method for guaranteeing good numerical behavior when the solution is expected to grow along the time variable. There is a wide variety of spatial problems that could benefit from this analysis. (C) 2011 Elsevier Ltd. All rights reserved.  
  Address [Gonzalez, E; Villena, MJ] Univ Adolfo Ibanez, Fac Sci & Engn, Santiago, Chile, Email:  
  Corporate Author Thesis  
  Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0898-1221 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000292573000005 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 155  
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