Browsing by Author "Bohner,M."

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Citation - Scopus: 6
The Euler Method for Dynamic Equations on Time Scales
(Cambridge Scientific Publishers, 2021) Bohner,M.; Erhan,İ.M.; Georgiev,S.G.; 01. Atılım University
In this paper, we generalize the Euler method for dynamic equations on time scales. We give estimates for the local and global truncation errors. We apply the method to specimen examples and provide numerical results to support our theoretical discussion. © 2021. All Rights Reserved.
Citation - Scopus: 26
Lyapunov Inequalities and Applications
(Springer International Publishing, 2021) Agarwal,R.P.; Bohner,M.; Özbekler,A.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
This book provides an extensive survey on Lyapunov-type inequalities. It summarizes and puts order into a vast literature available on the subject, and sketches recent developments in this topic. In an elegant and didactic way, this work presents the concepts underlying Lyapunov-type inequalities, covering how they developed and what kind of problems they address. This survey starts by introducing basic applications of Lyapunov's inequalities. It then advances towards even-order, odd-order, and higher-order boundary value problems; Lyapunov and Hartman-type inequalities; systems of linear, nonlinear, and quasi-linear differential equations; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, half-linear, and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamic systems. Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations. Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content. © Springer Nature Switzerland AG 2021. All rights reserved.