In the current work we consider the numerical solutions of equations ofstationary states for a general class of the spatial segregation ofreaction-diffusion systems with $m\geq 2$ population densities. We introduce adiscrete multi-phase minimization problem related to the segregation problem,which allows to prove the existence and uniqueness of the corresponding finitedifference scheme. Based on that scheme, we suggest an iterative algorithm andshow its consistency and stability. For the special case $m=2,$ we show thatthe problem gives rise to the generalized version of the so-called two-phaseobstacle problem. In this particular case we introduce the notion of viscositysolutions and prove convergence of the difference scheme to the uniqueviscosity solution. At the end of the paper we present computational tests, fordifferent internal dynamics, and discuss numerical results.
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机译：在当前的工作中，我们考虑种群为$ m \ geq 2 $的反应扩散系统空间隔离的一般类的平稳状态方程的数值解。我们引入了一个与分离问题有关的离散多相最小化问题，从而证明了相应的有限差分方案的存在性和唯一性。基于该方案，我们提出了一种迭代算法，并展示了其一致性和稳定性。对于特殊情况$ m = 2，$，我们表明该问题引起了所谓的两相障碍问题的广义形式。在这种特殊情况下，我们引入了粘度溶液的概念，并证明了差分方案对唯一粘度溶液的收敛性。在本文的最后，我们提出了计算测试，不同的内部动力学，并讨论了数值结果。
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