Reaction diffusion equations and quadratic convergence. (1997)

• Record Type: Journal Article
• Authors: Vatsala, A. S.; Mahrous, Mohamed A.; Alkahby, Hadi Yahya
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 10:Number 2(1997)
• Page Start: 179
• Page End: 186
• Publication Date: 1997
• Subjects: generalized quasilinearization -- upper and lower solutions; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S104895339700021X
• Languages: English
• ISSNs: 1048-9533

Abstract

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.