Line element method of solving singular integral equations

Anushree Samanta, Rumpa Chakraborty and Sudeshna Banerjea ()
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Anushree Samanta: Jadavpur University
Rumpa Chakraborty: Diamond Harbour Women’s University
Sudeshna Banerjea: Jadavpur University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 2, 528-541

Abstract: Abstract The work in this paper is concerned with application of a very simple numerical technique called line element method to solve singular integral equations with weakly singular kernel and hypersingular kernel. Of the integral equations considered here are first kind Abel integral equation and integral equation with log kernel and hypersingular integral equations of first and second kind. In this method, the range of integration as well as the interval of definition of the integral equation are discretised into finite number of small subintervals and the unknown function satisfying the integral equation is assumed to be constant in each small subinterval. This reduces the integral equations to a system of algebraic equations which is then solved to obtain the unknown function in each subinterval. The method is illustrated with examples. It is observed that a very accurate result is obtained by applying this method. The error analysis for this method is also given.

Keywords: Line element method; Abel integral equation; Integral equation with log kernel; hypersingular integral equation; Error analysis (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00115-7

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