New Results on the Quasilinearization Method for Time Scales

Şahap Çetin (), Yalçın Yılmaz and Coşkun Yakar
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Şahap Çetin: Department of Mathematics, Faculty of Sciences, Sakarya University, 54050 Sakarya, Turkey
Yalçın Yılmaz: Department of Mathematics, Faculty of Sciences, Sakarya University, 54050 Sakarya, Turkey
Coşkun Yakar: Department of Mathematics, Faculty of Sciences, Gebze Technical University, 41400 Kocaeli, Turkey

Mathematics, 2024, vol. 12, issue 14, 1-13

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.

Keywords: quasilinearization; quadratic convergence; weak convergence; extremal solutions; time scale (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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