tailieunhanh - báo cáo hóa học:" Research Article Approximation of Solutions for Second-Order m-Point Nonlocal Boundary Value Problems via the Method of Generalized Quasilinearization"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Approximation of Solutions for Second-Order m-Point Nonlocal Boundary Value Problems via the Method of Generalized Quasilinearization | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 929061 17 pages doi 2011 929061 Research Article Approximation of Solutions for Second-Order m-Point Nonlocal Boundary Value Problems via the Method of Generalized Quasilinearization Ahmed Alsaedi Department of Mathematics Faculty of Science King Abdulaziz University . Box 80203 Jeddah 21589 Saudi Arabia Correspondence should be addressed to Ahmed Alsaedi aalsaedi@ Received 11 May 2010 Revised 29 July 2010 Accepted 2 October 2010 Academic Editor Gennaro Infante Copyright 2011 Ahmed Alsaedi. 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. 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. 1. Introduction The monotone iterative technique coupled with the method of upper and lower solutions 1-7 manifests itself as an effective and flexible mechanism that offers theoretical as well as constructive existence results in a closed set generated by the lower and upper solutions. In general the convergence of the sequence of approximate solutions given by the monotone iterative technique is at most linear 8 9 . To obtain a sequence of approximate solutions converging quadratically we use the method of quasilinearization 10 . This method has been developed for a variety of problems 11-20 . In view of its diverse applications this approach is quite an elegant and easier for application algorithms. The subject of multipoint nonlocal boundary conditions initiated by Bicadze and Samarskii 21 has been addressed by many authors for instance 22-32 . The multipoint boundary conditions .