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Quasilinearization of dynamic equations on time scales involving the sum of three functions

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Wang, P.
Wu, Yong Hong
Date
2011
Type
Journal Article

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Wang, Peiguang and Wu, Yonghong. 2011. Quasilinearization of dynamic equations on time scales involving the sum of three functions. International Journal of Pure and Applied Mathematics. 70 (6): pp. 843-854.
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International Journal of Pure and Applied Mathematics
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Department of Mathematics and Statistics
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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 >= 1).