Abstract
In this paper, the method of generalized quasilinearization has been extended to reaction diffusion equations. The extension includes earlier known results as special cases. The earlier results developed are when (i) the right-hand side function is the sum of a convex and concave function, and (ii) the right-hand function can be made convex by adding a convex function. In our present result, if the monotone iterates are mildly nonlinear, we establish the quadratic convergence as in the quasilinearization method. If the iterates are totally linear then the iterates converge semi-quadratically.