一类反应扩散方程组的保持正性的差分格式

A Positivity-Preserving Difference Scheme for Reaction-Diffusion Systems

本文研究一类具有正解的反应扩散方程组的有限差分解法.构造了一个保持正性的差分格式.利用离散的最大值原理证明了差分格式解的非负性,有界性及差分格式的无条件稳定性.这些估计的证明不依赖于微分方程的解而仅仅与初边值条件有关.当微分方程的解适当光滑时,证明了差分格式的一致收敛性.最后给出了数值计算结果,并与以往方法进行了比较.计算结果说明了本文给出的方法的有效性.

Numerical solution of a finite difference scheme for reaction-diffusion systems with positive solution is investigated.The difference scheme constructed in this paper is positivity-preserving and unconditionally stable.These estimates have been obtained without using any properties of the solution of differential equations and depend only upon initial boundary datum.It is proved that the difference scheme is uniformly convergent if the solution of differential equation is appropriate smooth.Finally,some num...