Numerical Analysis and Applicable Mathematics
Title
A Numerical Scheme for Solving Convolution Type Volterra Integral Equations
Authors
Marjan Uddin,* Muhammad Mehran and Qaiser Iqbal
Department of Basic Sciences and Islamiat, University of engineering and technology Peshawar, Pakistan.
*Corresponding author E-mail address: ddnmarjan@gmail.com (Marjan Uddin)
Article History
Publication details: Received: 26th December 2020; Revised: 31st January 2021; Accepted: 30th August 2022; Published: 14th September 2022
Cite this article
Uddin M.; Mehran M.; Iqbal Q. A Numerical Scheme for Solving Convolution Type Volterra Integral Equations. Numer. Anal. Appl. Math., 2022, 3(6), 10-14.
Abstract
In this paper a numerical scheme is constructed for approximation of Volterra integral equation of convolution type. The numerical scheme is based on Laplace transform and quadrature. By the use of Laplace transform the integral equation is converted to a system of equations in the transformed space and then inverse Laplace is numerically approximated in the complex plane along hyperbolic contour. The numerical scheme and its error estimate is discussed and validated for various VIE problems.
Keywords
Volterra; Integral Equation (VIE); Laplace Transform; Quadrature Method; Trapezoidal Rule; Hyperbolic Contour