New Results on the Quasilinearization Method for Time Scales

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 c...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-07, Vol.12 (14), p.2207
Main Authors: Çetin, Şahap, Yılmaz, Yalçın, Yakar, Coşkun
Format: Article
Language:English
Subjects:
Approximation
Boundary value problems
Dynamical systems
extremal solutions
Integral equations
Linear equations
Ordinary differential equations
quadratic convergence
quasilinearization
Time
time scale
weak convergence
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12142207