The generalized quasi-linearization method for reaction diffusion equations on an unbounded domain
The authors extend the method of generalized quasilinearization to reaction diffusion equations on an unbounded domain. The iterates, which are solutions of linear equations starting from lower and upper solutions, converge uniformly and monotonically to the unique solution of a nonlinear reaction diffusion equation in an unbounded domain. Initially an existence theorem for the linear nonhomogeneous reaction diffusion equation in an unbounded domain has been proved under improved conditions. The quadratic convergence has been proved by using a comparison theorem for reaction diffusion equations with ordinary differential equations. This avoids the computational complexity of the quasilinearization method, since the computation of the Green's function at each stage of the iterates is avoided.
scientific article; zbMATH DE number 1346381