IJPAM: Volume 70, No. 6 (2011)
TIME SCALES INVOLVING THE SUM OF THREE FUNCTIONS
College of Electronic and Information Engineering
Baoding, 071002, P.R. CHINA
Department of Mathematics and Statistics
Curtin University of Technology
GPO Box U1987, Perth, WA6845, AUSTRALIA
Abstract. In this paper, we present and discuss a method of quasilinearization, coupled with the method of upper and lower solutions for the solutions of a class of two-point boundary value problem of dynamic equations on time scales concerning the sum of three functions. A monotone iterative scheme whose elements converge rapidly to the unique solution of the problem is established, and the convergence is shown to be of order .
Received: March 7, 2011
AMS Subject Classification: 34B15, 39A12
Key Words and Phrases: time scales, dynamic equations, quasilinearization, rapid convergence, upper and lower solutions
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395