Two-grid quasilinearization approach for a class of nonlinear evolution systems.

This paper deals with numerical solution of nonlinear evolution systems modelling reaction-diffusion-convection processes in the natural and engineering sciences. Using Rothe method, we concentrate on construction of effective solution of the corresponding nonlinear stationary problems on each time level. First we discuss the solution by Newton-Bellman & Kalaba quasilinearization. Then, on this base high order and cheaper (with respect to computational cost) algorithms are proposed. Numerical results for a parabolic-hyperbolic system of two equations from the filtration are discussed. [ABSTRACT FROM AUTHOR]