Journal of Applied Mathematics and Stochastic Analysis
Volume 10 (1997), Issue 2, Pages 179-186
Reaction diffusion equations and quadratic convergence
1University of Southwestern Louisiana, Department of Mathematics, Lafayette 70504-1010, LA, USA
2Dillard University, Department of Mathematics, New Orleans 70122-3097, LA, USA
Received 1 January 1996; Revised 1 August 1996
Copyright © 1997 A. S. Vatsala et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.