Numerical investigation of generalized quasilinearization method for reaction diffusion systems

Abstract

In, we have developed generalized quasilinearization method for reaction diffusion systems when the forcing functions are the sum of convex and concave functions. The solutions of the corresponding linear systems converge monotonically, uniformly and quadratically to the unique solution of the nonlinear problem. As a byproduct of our result, we have discussed the reaction diffusion system when the forcing function satisfies mixed quasimonotone property. In this paper, we have established the application of the theoretical results developed in with numerical examples. We also demonstrate the consistency of the finite different scheme and discuss the stability and convergence of the scheme for the examples considered here.