Browsing by Author "Georgiev,S.G."

Now showing 1 - 4 of 4

Citation - Scopus: 5
Adomian Polynomials Method for Dynamic Equations on Time Scales
(DergiPark, 2021) Georgiev,S.G.; Erhan,I.M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
A recent study on solving nonlinear differential equations by a Laplace transform method combined with the Adomian polynomial representation, is extended to the more general class of dynamic equations on arbitrary time scales. The derivation of the method on time scales is presented and applied to particular examples of initial value problems associated with nonlinear dynamic equations of first order. © 2021, DergiPark. All rights reserved.
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: 1
Numerical Analysis on Time Scales
(De Gruyter, 2022) Georgiev,S.G.; Erhan,I.M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Mathematical models cannot be solved using the traditional analytical methods for dynamic equations on time scales. These models must be dealt with using computational methods. This textbook introduces numerical methods for initial value problems for dynamic equations on time scales. Hands-on examples utilizing MATLAB and practical problems illustrate a wide variety of solution techniques. This textbook discusses the design, analysis and applications of computational techniques for dynamic equations on time scales. Hands-on examples utilizing MATLAB are provided as well as end of chapter problems. © 2022 Walter de Gruyter GmbH, Berlin/Boston. All rights reserved.
Citation - Scopus: 5
SERIES SOLUTION METHOD FOR CAUCHY PROBLEMS WITH FRACTIONAL Δ-DERIVATIVE ON TIME SCALES
(Element D.O.O., 2019) Georgiev,S.G.; Erhan,I.M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper we introduce a series solution method for Cauchy problems associated with Caputo fractional delta derivatives on time scales with delta differentiable graininess function. We also apply the method to Cauchy problems associated with dynamic equations and present some illustrative examples. © The Author(s) 2019.