TAILIEUCHUNG - Báo cáo sinh học: " Research Article Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales Rahmat Ali Khan1 and Mohammad Rafique2 1"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales Rahmat Ali Khan1 and Mohammad Rafique2 1 | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 841643 11 pages doi 2010 841643 Research Article Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales Rahmat Ali Khan1 and Mohammad Rafique2 1 Centre for Advanced Mathematics and Physics National University of Sciences and Technology NUST H-12 Islamabad 46000 Pakistan 2 Department of Basic Sciences College of Electrical and Mechanical Engineering National University of Sciences and Technology NUST Peshawar Road Rawalpindi 46000 Pakistan Correspondence should be addressed to Mohammad Rafique mrdhillon@ Received 24 August 2009 Revised 13 May 2010 Accepted 2 June 2010 Academic Editor Ondrej Dosly Copyright 2010 R. A. Khan and M. 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. 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 xAA f f t xơ f t 10 1L 10 11 n T W01 - 0 yi 2 111 - vm71 Í 1 t 0 11 vm-1 1 dpvpld f t 0 1JT _ 0 1J n T X 0f 0 x ư 1 z Ịi 1 aiX nif ni t 0 1 T 1i 1 ai ù 1 are developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the problem is obtained. 1. Introduction Many dynamical processes contain both continuous and discrete elements simultaneously. Thus traditional mathematical modeling techniques such as differential equations or difference equations provide a limited understanding of these types of models. A simple example of this hybrid continuous-discrete behavior appears in many natural populations for example insects that lay their eggs at the end of the season just before the generation dies out with the eggs laying dormant hatching at the start of the next season giving .

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