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Author  |
Gonzalez, E.; Villena, M.J. |
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Title |
Spatial attrition modeling: Stability conditions for a 2D + t FD formulation |
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Year |
2011 |
Publication |
Computers & Mathematics With Applications |
Abbreviated Journal |
Comput. Math. Appl. |
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Volume |
61 |
Issue |
11 |
Pages |
3246-3257 |
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Keywords |
PDE; Stability; Reaction-diffusion; Spatial attrition modeling |
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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. |
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Address |
[Gonzalez, E; Villena, MJ] Univ Adolfo Ibanez, Fac Sci & Engn, Santiago, Chile, Email: eduardo.gonzalez@uai.cl |
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Publisher |
Pergamon-Elsevier Science Ltd |
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English |
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0898-1221 |
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Notes |
WOS:000292573000005 |
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Call Number |
UAI @ eduardo.moreno @ |
Serial |
155 |
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