The generalized quasi-linearization method for reaction diffusion equations on an unbounded domain

The method of generalized quasi-linearization has been well, developed for ordinary differential equations. In this paper, we extend the method of gen eralized quasi-linearization to reaction diffusion equations on an unbounde d domain. The iterates, which are solutions of linear equations starting fr om lower and upper solutions, converge uniformly and monotonically to the u nique solution of the nonlinear reaction diffusion equation in an unbounded domain. Initially an existence theorem for the linear nonhomogeneous react ion diffusion equation in an unbounded domain has been proved under improve d conditions. The quadratic convergence has been proved by using a comparis on theorem of reaction diffusion equations with ordinary differential equat ions. This avoids the computational complexity of the quasi-linearization m ethod, since the computation of Green's function at each stage of the itera tes is avoided. (C) 1999 academic Press.