Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 2, Pages 117-122

Quasilinearization for some nonlocal problems

Yunfeng Yin

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.


The method of generalized quasilinearization [4] is applied to study semilinear parabolic equation utLu=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.