关键词：扩散系统；非负变量算法；数值方法求解系统
摘 要：We present a Cartesian grid nite di erence numerical method for solving a system ofreaction-di usion initial boundary value problems with Neumann type boundary conditions.The method utilizes adaptive time-stepping, which guarantees stability and non-negativityof the solutions. The latter property is critical for models in biology where solutions rep-resent physical measurements such as concentration. The level set representation of theboundary enables us to handle domains with complicated geometry with ease. We pro-vide numerical validation of our method on synthetic and biological examples. Empiricaltests demonstrate second order convergence rate in the L1- and L2-norms, as well as in theL1-norm for many cases.