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Reaction diffusion equations and quadratic convergence. (English) Zbl 0884.35063
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. If the monotone iterates are mildly nonlinear, the authors obtain the quadratic convergence as in the quasilinearization method. If the iterates are totally linear then the iterates converge semi-quadratically.
MSC:
35K57 Reaction-diffusion equations
35A35 Theoretical approximation in context of PDEs
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