Approximate Numerical Solutions for Linear Volterra Integral Equations Using Touchard Polynomials

Main Article Content

Jalil Talab Abdullah
https://orcid.org/0000-0002-6847-3635

Abstract

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

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Approximate Numerical Solutions for Linear Volterra Integral Equations Using Touchard Polynomials. Baghdad Sci.J [Internet]. 2020 Dec. 1 [cited 2024 Mar. 28];17(4):1241. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3753
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article

How to Cite

1.
Approximate Numerical Solutions for Linear Volterra Integral Equations Using Touchard Polynomials. Baghdad Sci.J [Internet]. 2020 Dec. 1 [cited 2024 Mar. 28];17(4):1241. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3753

References

Eleonora M, Antonia V. Stability and Boundless of Numerical Approximations to Volterra Integral Equations. APPL NUMER MATH. 2017 June; 116: 230-237

Hashmi M. S, Khan N, Iqbal S. Numerical Solutions of Weakly Singular Volterra Integral Equations Using the Optimal Homotopy Asymptotic Method. COMPUT MATH APPL. 2012; 64 (2012) : 1567–1574.

Abdul J. J. Introduction to Integral Equations with Applications. New York: MARCEL DEKKER; 1985. 73- 74 P.

Abdul-Majid W. Linear and Nonlinear Integral Equations Methods and Applications. Heidelberg Dordrecht London New-York: Springer; 2011. 35-36 p.

Mohamed M.S, Gepreel K. A, Al-Malki F. A, Al-Humyani M. Approximate solutions of the generalized Abel’s integral equations using the extension Khan’s homotopy analysis transformation method. J APPL MATH. 2015. 9 pages. Available from: https://doi.org/10.1155/2015/357861

Muftahov I, Tynda A, Sidorov D. Numerical Solution of Volterra Integral Equations of the First Kind with Discontinuous Kernel. J COMPUT APPL MATH. 2017 Mar 15; 313(15): 119-128

Marjan U, Muhammad T. On the Approximation of Volterra Integral Equations with Highly Oscillatory Bessel Kernels via Laplace Transform and Quadrature. AEJ. 2019; 58(2019): 413-417.

Hashmi M. S, Khan N, Iqbal S. Numerical Solutions of Weakly Singular Volterra Integral Equations Using the Optimal Homotopy Asymptotic Method. COMPUT MATH APPL.2012 Sept; 64 (6):1567-1574.

Can H, Martin S. Spectral Galerkin Methods for a Weakly Singular Volterra Integral Equation of the Second Kind. IMA JNA. 2017 July; 37(3): 1411-1436.

Xiao-yong Z. A Multistep Legendre Pseudo-Spectral Method for Volterra Integral Equations. APPL MATH COMPUT. 2016 Feb 1; 274: 480-494.

Nazir A, Usman M, Mohyud-Din ST.Touchard Polynomials Method for Integral Equations. Int. J. Modern Theo. Physics, 2014; 3(1): 74-89.

Paris R. B. The Asymptotes of the Touchard Polynomials: a uniform approximation. Math. Æterna. 2016 Jun 28; 6(5): 765-779.

Miloud M, Mohammed S. M. Touchard Polynomials, Partial Bell Polynomials and Polynomials of Binomial Type. Journal of Integer Sequences. 2011 Mar 25; 14(2011): 1-9.

Sun ZW, Zagier D. ON A curious Property of Bell Numbers. Bull. Aust. Math. Soc. 2011; 84: 153-158

Rani D, Mishra V. Solutions of Volterra Integral and Integro-Differential Equations Using Modified Laplace Adomian Decomposition Method. JAMSI. 2019 June; 15 (1):1-18

Maleknejad K, Hashemizadeh E, Ezzati R. A new Approach to the Numerical Solution of Volterra Integral Equations by Using Bernstein’s Approximation. Commun Nonlinear Sci Numer Simulat. 2011; 16 (2011): 647–655

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