On volterra integral equations of the first kind by using Elzaki transform

Abstract

In this paper, we study the Volterra integral equations of the first kind with a bulge function. The Elzaki transform, inverse Elzaki transform and the convolution theorem are used in this study to derive the exact solution. The Simpson’s quadrature rule is employed to find the numerical solutions. kind, converted the linear Volterra integral equations of the first kind to a recurrence relation and shown that the estimates have a good degree of accuracy. Recently, Haarsa and Pothat [6] introduced the Volterra integral equations of the first kind with the bulge function. The exact solution is obtained by using the Laplace transform. In this study, we experience the Volterra integral equations of the first kind with a bulge function. The exact solution is derived by using the Elzaki transform, inverse Elzaki transform, the convolution theorem and Taylor series expansion. The Simpson’s quadrature rule is used to find the numerical solutions. © 2017 Pushpa Publishing House, Allahabad, India.