Approximation of Solutions for Second-Order m-Point Nonlocal Boundary Value Problems via the Method of Generalized Quasilinearization

Abstract

We discuss the existence and uniqueness of the solutions of a second-order m-point nonlocal boundary value problem by applying a generalized quasilinearization technique. A monotone sequence of solutions converging uniformly and quadratically to a unique solution of the problem is presented.

On nonlocal three-point boundary value problems of Duffing equation with mixed nonlinear forcing terms

“…This development was so significant that it attracted the attention of many researchers, and the method was extensively developed and applied to a wide range of initial and boundary value problems for different types of differential equations. A detailed description of the quasilinearization method and its applications can be found in the monograph [9] and the papers [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and the references therein.…”