Generalized Quasilinearization Method for Reaction Diffusion Systems

Abstract

In this paper, we develop generalized quasilinearization method for reaction diffusion systems when the forcing function is the sum of a convex and concave functions. Due to the splitting of the forcing function we have four different types of coupled upper and lower solutions. We have developed iterates which converge monotonically, uniformly and quadratically to the unique solution of the reaction diffusion systems.