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Higher even-order convergence and coupled solutions for second-order boundary value problems on time scales

✍ Scribed by Peiguang Wang; Haixia Wu; Yonghong Wu

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 443 KB
Volume: 55
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2007.06.026

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✦ Synopsis

In this paper, for a second-order boundary value problem on time scales, a method of generalized quasilinearization, under coupled upper and lower solutions, is discussed. An attempt for the method is to establish sufficient conditions for generating monotone iterative schemes whose elements converge rapidly to the unique solution of the given problem. Furthermore, the convergence is of order k (k ≥ 2), which is even. Finally, two examples are provided to illustrate our results.

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