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Numerical Analysis and Applicable Mathematics

Research Article

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.

AP-NAAM-2021-01-023_(R1)_GA.jpg

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

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