Advances in Difference Equations
Volume 2010 (2010), Article ID 841643, 11 pages
doi:10.1155/2010/841643
Research Article

Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales

Rahmat Ali Khan1 and Mohammad Rafique2

1Centre for Advanced Mathematics and Physics, National University of Sciences and Technology (NUST), H-12, Islamabad 46000, Pakistan
2Department of Basic Sciences, College of Electrical and Mechanical Engineering, National University of Sciences and Technology (NUST), Peshawar Road, Rawalpindi 46000, Pakistan

Received 24 August 2009; Revised 13 May 2010; Accepted 2 June 2010

Academic Editor: Ondřej Došlý

Copyright © 2010 Rahmat Ali Khan and Mohammad Rafique. 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 upper and lower solutions and the generalized quasilinearization technique for second-order nonlinear m-point dynamic equations on time scales of the type xΔΔ(t)=f(t,xσ), t∈[0,1]T=[0,1]∩T, x(0)=0, x(σ2(1))=∑i=1m-1αix(ηi), ηi∈(0,1)T, ∑i=1m-1αi≤1, are developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the problem is obtained.