Approximate solution of Abel integral equation in Daubechies wavelet basis

Jyotirmoy Mouley; M. M. Panja; B. N. Mandal

doi:10.4067/S0719-06462021000200245

DOI:

https://doi.org/10.4067/S0719-06462021000200245

Abstract

This paper presents a new computational method for solving Abel integral equation (both first kind and second kind). The numerical scheme is based on approximations in Daubechies wavelet basis. The properties of Daubechies scale functions are employed to reduce an integral equation to the solution of a system of algebraic equations. The error analysis associated with the method is given. The method is illustrated with some examples and the present method works nicely for low resolution.

Keywords

Abel integral equation , Daubechies scale function , Daubechies wavelet , Gauss-Daubechies quadrature rule

Jyotirmoy Mouley Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata-700 009, India.
M. M. Panja Department of Mathematics, Visva-Bharati, Santiniketan, West Bengal, 731235, India.
B. N. Mandal Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata-700108, India.

Pages: 245–264
Date Published: 2021-08-01
Vol. 23 No. 2 (2021)

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