Analytical solution of linear Volterra integral equations of first and second kind by using Elzaki transform

R.B. Thete; Arihant Jain

doi:10.26637/MJM0804/0173

Abstract

In recent decades, the use of integral transforms becomes a powerful tool to solve problems in science and technology. Integral transforms have been used to find the solution to problems governed by ordinary and partial differential equations and special types of integral equations. The integral transforms aim to transform a given problem into a simpler form that can be solved easily. The integral transforms are used to find the solution to initial value problems. The integral transforms are also useful in the evaluation of certain integrals and the solution of certain differential equations, partial differential equations, and integral equations. In this paper, we have applied a new integral transform, i.e., Elzaki Transform for the solution of linear Volterra integral equation of the first and second kind and some numerical examples discussed for the validity of results.

Keywords:

Elzaki transform, Inverse Elzaki transform, Convolution theorem, Volterra integral equation, Linear Volterra integral equation

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

R.B. Thete Department of Mathematics, Pravara Rural Engineering College, Loni-413736, Maharashtra, India.
Arihant Jain Department of Mathematics, Dr A.P.J. Abdul Kalam University, Indore-452016, Madhya Pradesh, India.

Pages: 2315-2319
Date Published: 01-10-2020
Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

T.M. Elzaki, The new integral transform Elzaki Transform, Global Journal of Pure and Applied Mathematics, 1(2011), 57-64.

T.M. Elzaki, S.M. Ezaki and E.A. Elnour, On the new integral transform Elzaki Transform fundamental properties investigations and applications, Global Journal of Mathematical Sciences: Theory and Practical, 4(1)(2012), $1-13$.

H. Kim, The time shifting theorem and the convolution for Elzaki transform, International Journal of Pure and Applied Mathematics, 87(2)(2013), 261-271.

T.M. Elzaki and S.M. Ezaki, On the connections between Laplace and Elzaki transforms, Advances in Theoretical and Applied Mathematics, 6(1)(2011), 1-11.

T.M. Elzaki and S.M. Ezaki, On the Elzaki transform and ordinary differential equation with variable coefficients, Advances in Theoretical and Applied Mathematics, $6(1)(2011), 41-46$.

T.M. Elzaki and S.M. Ezaki, Applications of new transform Elzaki transform to partial differential equations, Global Journal of Pure and Applied Mathematics, $7(1)(2011), 65-70$.[7] A.M. Shendkar and P.V. Jadhav, Elzaki transform: A solution of differential equations, International Journal of Science, Engineering and Technology Research, 4(4)(2015), 1006-1008.

[ S. Agarwal, Elzaki transform of Bessel's functions, Global Journal of Engineering Science and Researches, 5(8)(2018), 45-51.

S. Agarwal, N. Sharma and R. Chauhan, Application of Mahgoub transform for solving linear Volterra integral equations of first kind, Global Journal of Engineering Science and Researches, 5(9)(2018), 154-161.

S. Agarwal, D.P. Singh, N. Asthana, and A.R. Gupta, Application of Elzaki transform for solving population growth and decay problems, Journal of Emerging Technologies and Innovative Research, 5(9)(2018), 281-284.

S. Agarwal, N. Sharma, and R. Chauhan, Application of Kamal transform for solving linear Volterra integral equations of first kind, International Journal of Research in Advent Technology, 6(8)(2018), 2081-2088.

P.S. Kumar, C. Saranya, M.G. Gnanavel, and A. Viswanathan, Applications of Mohand transform for solving linear Volterra integral equations of first kind, International Journal of Research in Advent Technology, 6(10)(2018), 2786-2789.

A.M. Wazwaz, Linear and Nonlinear Integral Equations: Methods and Applications, Springer, New York, USA, 2011.

L. M. Delves and J. L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, Cambridge, 1985.

R.B. Thete, Temperature distribution of an inverse steady state thermo elastic problem of thin rectangular plate by numerical method, IOSR Journal of Mathematics, $11(1)(2015), 36-39$

M. Tarik, Elzaki Adil Mousa, Solution of Volterra integrodifferential equation by triple Laplace Transform, Irish International Journal of Science & Research, 3(4)(2019), $1-8$.

R.B. Thete, Estimation of temperature distribution and thermal stress analysis of composite circular rod by finite element method, Elixir Appl. Math., 95(2016), 1-10.