Combined Monotone Lterative Methods For Nonlinear Finite Difference Reaction-Diffusion-Convection Equations

This paper is concerned with the computational algorithms for finite difference systems of a class of nonlinear reaction-diffusion-convection equations with nonlinear boundary conditions.The investigation is devoted to the finite difference systems for both the time-dependent problem and its corresponding steady-state problem.A combined monotone iterative method is presented by using the method of upper and lower solutions.It is shown that the sequence of iterations converges monotonically to a unique solution of the system in a sector between a pair of upper and lower solutions,and the monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration. The rate of convergence of the iterations is estimated explicitly by infinity norm,and the order of convergence attains at p+2 where p＞1 is a positive integer depending on the construction of the iterative method.An application is given to an enzyme substrate reaction model,and some numerical results are presented to illustrate the effectiveness of the proposed method.