Stability Analysis for Spatial Attrition with n Forces

Close combat between two forces can be modelled through a set of two coupled partial differential equations, of second order in space and first order in time. That problem has been studied and shows a way to find stable solutions by means of a careful selection of the discretization both in time and space and through the use of a simple transformation. The results are generalized here for more interacting forces. It is found that the eigenvalues of the matrix that represent the system dynamics together with the time step size shape up the stability coefficients.