Homotopy Approach for Integrodifferential Equations

Damian Słota, Edyta Hetmaniok, Roman Wituła, Krzysztof Gromysz and Tomasz Trawiński
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Damian Słota: Institute of Mathematics, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
Edyta Hetmaniok: Institute of Mathematics, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
Roman Wituła: Institute of Mathematics, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
Krzysztof Gromysz: Department of Building Structures, Faculty of Civil Engineering, Silesian University of Technology, 44-100 Gliwice, Poland
Tomasz Trawiński: Department of Mechatronics, Faculty of Electrical Engineering, Silesian University of Technology, 44-100 Gliwice, Poland

Mathematics, 2019, vol. 7, issue 10, 1-15

Abstract: In this paper, we present the application of the homotopy analysis method for solving integrodifferential equations. In this method, a series is created, the successive elements of which are determined by calculating the appropriate integral of the previous element. In this elaboration, we prove that, if this series is convergent, then its sum is the solution of the objective equation. We formulate and prove the sufficient condition of this convergence, and we give also the estimation of error of an approximate solution obtained by taking the partial sum of the considered series. Moreover, we present in this paper the example of using the investigated method for determining the vibrations of the freely supported reinforced concrete beam as well as for solving the equation of movement of the electromagnet jumper mechanical system.

Keywords: integrodifferential equation; homotopy analysis method; convergence; error estimation; electromagnet jumper; vibrations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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