New Results on the Quasilinearization Method for Time Scales-Reference-Cited by-同舟云学术

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New Results on the Quasilinearization Method for Time Scales

Published:2024-07-14 Issue:14 Volume:12 Page:2207
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Çetin Şahap¹,Yılmaz Yalçın¹,Yakar Coşkun²

Affiliation:

1. Department of Mathematics, Faculty of Sciences, Sakarya University, 54050 Sakarya, Turkey

2. Department of Mathematics, Faculty of Sciences, Gebze Technical University, 41400 Kocaeli, Turkey

Abstract

We have developed the generalized quasilinearization method (QM) for an initial value problem (IVP) of dynamic equations on time scales by using comparison theorems with a coupled lower solution (LS) and upper solution (US) of the natural type. Under some conditions, we observed that the solutions converged to the unique solution of the problem uniformly and monotonically, and the rate of convergence was investigated.

Funder

Sakarya University and TUBITAK

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/14/2207/pdf

Reference25 articles.

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2. Lakshmikantham, V., and Koksal, S. (2003). Monotone Flows and Rapid Convergence, CRC Press.

3. Coupled solutions and monotone iterative techniques for some nonlinear IVPs on time scales;Lawrence;Nonlinear Anal. Real World Appl.,2003

4. Bohner, M., and Peterson, A. (2001). Dynamic Equations on Time Scales. An Introduction with Applications, Birkhäuser.

5. Quasilinearization approach for two point nonlinear boundary value problems on time scales;Atici;Rocky Mt. J. Math.,2005

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