Numerical Solution of Volterra Integral Equations Using Hosoya Polynomial

Year 2021, Volume: 6 Issue: 3, 110 - 117, 30.12.2021

Merve Zeynep Geçmen , Ercan Çelik , Mustafa Ali Dokuyucu

Abstract

In this study, Volterra integral equation is solved by Hosoya Polynomials. The solutions obtained
with Hosoya method were compared on the figure and table. And error analysis was done. Matlab has
been used to obtain results, tables and error analysis.

Keywords

Volterra Integral Equations, Hosoya Polynomial, Path Graphs

References

• M. A. Abdou, A. A. Soliman and M. A. Abdel–Aty, On a discussion of Volterra Fredholm integral equation with discontinuous kernel, Journal of the Egyptian Mathematical Society, 1-10, 2020.
• Ramane, H.S, Shiralashetti S.C., Mundewadi R.A and Jummannaver R.B., Numerical Solution of Fredholm Integral Equations Using Hosoya Polynomial of Path Graphs, American Journal of Numerical Analysis, Vol. 5, No. 1, 11-15, 2017.
• D. Stevanovic, Hosoya polynomial of composite graphs, Department of Mathematics, Faculty of Philosophy, Cirila i Metodija 2, Niˇs 18000, Yugoslavia.
• E. V. Konstantinova, M. V. Diudea, The Wiener polynomial derivatives and other topological indices in chemical research, Croat. Chem. Acta 73, 383-403, 2000.
• G. Cash, S. Klavˇzar, M. Petkovˇsek, Three methods for calculation of the hyper–wiener index of molecular graphs, J.Chem. Inf. Comput. Sci. 43, 571-576, 2002.
• I. Gutman, Hosoya polynomial and the distance of the total graph of a tree, Publ. Elektrotehn. Fak. (Beograd) Ser. Mat.,10, 53-58, 1999.
• H. S. Ramane, K. P. Narayankar, S. S. Shirkol, A. B. Ganagi, Terminal Wiener index of line graphs, MATCH Commun. Math. Comput. Chem., 69, 775-782, 2013.
• N.Tratnika, P. Z. Pletersek, Relationship Between the Hosoya Polynomial and the Edge- Hosoya Polynomial of Trees, MATCH Commun. Math. Comput. Chem. 78, 181-187, 2017.
• S. Upadhyay and K. N. Rai, Integral equation, https://www.researchgate.net/publication/283829675, November, 2015.
• J. A.Zarnan, International Journal of Computer Science and Mobile Computing, Vol.5 Issue.7, pg. 509-514, July- 2016.
• S. Saha Ray and P. K. Sahu, Numerical Methods for Solving Fredholm Integral Equations of Second Kind, Hindawi Publishing Corporation ,Abstract and Applied Analysis, Volume 2013.
• Ar, N. and Farman, T., Hosoya Polynomial and Topological Indices of the Jahangir Graph J7,m, Journal of Applied and Computational Mathematics, 7, 1-5, 2018.
• Gecmen, MZ., and Celik, E., Numerical solution of Volterra–Fredholm integral equations with Hosoya polynomials, Mathematical Methods in the Applied Sciences, 44 (12), 2021.