Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 2, Pages 117-122
doi:10.1155/S1048953393000115
Quasilinearization for some nonlocal problems
Florida Institute of Technology, Department of Applied Mathematics, Melbourne 32901-6988, FL, USA
Received 1 February 1993; Revised 1 April 1993
Copyright © 1993 Yunfeng Yin. 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.
Abstract
The method of generalized quasilinearization [4] is applied to
study semilinear parabolic equation ut−Lu=f(t,x,u) with nonlocal
boundary conditions u(t,x)=∫Ωϕ(x,y)u(t,y)dy in this paper. The
convexity of f in u is relaxed by requiring f(t,x,u)+Mu2 to be convex
for some M>0. The quadratic convergence of monotone sequence is
obtained.