Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4634146 | Applied Mathematics and Computation | 2008 | 10 Pages |
Abstract
In the method of quasilinearization or the method of generalized quasilinearization we assume that âkf(t,x,u)âuk exists, where f(t,x,u) is the forcing function and obtain kth order of convergence. In this paper, we assume a weaker condition namely, âk-1f(t,x,u)âuk-1 exists and Lipschitzian in u and develop generalized quasilinearization method to reaction diffusion equations. The iterates will be different depending on âk-1f(t,x,u)âuk-1 is nondecreasing or nonincreasing in u and k being even or odd. Finally, we prove that the sequences generated by the generalized quasilinearization method converge to the unique solution of the nonlinear reaction diffusion equation and the convergence is of order k.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Tanya G. Melton, A.S. Vatsala,