The quasilinearization method in the system of reaction diffusion equations

Abstract

In this paper the method of generalized quasilinearization has been extended to system of reaction diffusion equations with initial and boundary conditions. Quadratic convergence of the sequences of lower and upper solutions to the unique solution of the nonlinear system of reaction diffusion equations has been proved. This has been achieved by using a comparison theorem of the system of reaction diffusion equations with the system of ordinary differential equations. Finally, numerical scheme for the generalized quasilinearization method has been developed for reaction diffusion systems.