IJPAM: Volume 70, No. 6 (2011)

QUASILINEARIZATION OF DYNAMIC EQUATIONS ON
TIME SCALES INVOLVING THE SUM OF THREE FUNCTIONS

Peiguang Wang$^1$, Yonghong Wu$^3$
$^1$College of Electronic and Information Engineering
Hebei University
Baoding, 071002, P.R. CHINA
$^2$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 $k+1$ $(k \geq 1)$.

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
Year: 2011
Volume: 70
Issue: 6