ACCELERATED MONOTONE ITERATIVE METHODS FOR FINITE-DIFFERENCE EQUATIONS OF REACTION-DIFFUSION

This paper is concerned with numerical methods for a finite difference system of reaction-diffusion-convection equation under nonlinear boun dary condition. Various monotone iterative methods are presented, and each of these methods leads to an existence-comparison theorem as well as a computational algorithm for numerical solutions. The monotone pr operty of the iterations gives improved upper and lower bounds of the solution in each iteration, and the rate of convergence of the iterati ons is either quadratic or nearly quadratic depending on the property of the nonlinear function. Application is given to a model problem fro m chemical engineering, and some numerical results, including a test p roblem with known analytical solution, are presented to illustrate the various rates of convergence of the iterations.