Quadratic approximation of solutions for boundary value problems with nonlocal boundary conditions
In this paper, using the quasilinearization method coupled with the method of upper and lower solutions, we study a class of second-order nonlinear boundary value problems with nonlocal boundary conditions. We establish some sufficient conditions under which corresponding monotone sequences converge uniformly and quadratically to the unique solution of the problem. An example is also included to illustrate the main result. (C) 2011 Elsevier Ltd. All rights reserved.
quasilinearization upper and lower solutions nonlinear boundary value problem quadratic convergence