Finite difference solutions of reaction diffusion equations with continuous time delays (Q1600386)

The nonlinear finite difference system \[ (I+kA)u_n=u_{n-1}+k f_n(u_n,HJ*u_n)+g_n,\quad n=1,2,\dots n_n=\eta_n,\quad n=0,-1,\dots,-s, \] where \(u_n\in \mathbb{R}^N\), \(A_n\) is an \(N\times N\) matrix and \(f_n\), \(g_n\) and \(\eta_n\) are given functions, is considered as a finite difference approximation of some initial-boundary value problem for a reaction diffusion system with continuous delay. Using the method of lower and upper solution the existence of unique solution is shown. Various monotone iterative schemes are used for computation of numerical solution. Some applications are included.