Title: Boundary element approach of solving Fredholm and Volterra integral equations

Authors: Sudeshna Banerjea; Rumpa Chakraborty; Anushree Samanta

Addresses: Department of Mathematics, Jadavpur University, Kolkata, 700032, India ' Department of Mathematics, Diamond Harbour Women's University South 24 Parganas, 743368, India ' Department of Mathematics, Jadavpur University, Kolkata, 700032, India

Abstract: A simple numerical technique namely boundary element method (BEM) is employed here to solve Fredholm and Volterra integral equations of the second kind. In this method, the integral equation is converted into a system of linear algebraic equations by discretising the range of the integration and interval of definition into a finite number of line elements. By solving the system of linear equations by standard technique the solution of the integral equation is obtained for points in each line element. The method is computationally very simple and gives quite accurate results.

Keywords: Fredholm and Volterra integral equation; BEM; boundary element method; line elements; system of linear equations; approximate solution; relative error.

DOI: 10.1504/IJMMNO.2019.096907

International Journal of Mathematical Modelling and Numerical Optimisation, 2019 Vol.9 No.1, pp.1 - 11

Received: 15 Aug 2017
Accepted: 27 Nov 2017
Published online: 13 Dec 2018 *

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