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A novel technique based on Bernoulli wavelets for numerical solutions of two-dimensional Fredholm integral equation of second kind

A novel technique based on Bernoulli wavelets for numerical solutions of two-dimensional Fredholm... A novel technique based on Bernoulli wavelets has been proposed to solve two-dimensional Fredholm integral equation of second kind. Bernoulli wavelets have been created by dilation and translation of Bernoulli polynomials. This paper aims to introduce properties of Bernoulli wavelets and Bernoulli polynomials.Design/methodology/approachTo solve the two-dimensional Fredholm integral equation of second kind, the proposed method has been used to transform the integral equation into a system of algebraic equations.FindingsNumerical experiments shows that the proposed two-dimensional wavelets technique can give high-accurate solutions and good convergence rate.Originality/valueThe efficiency of newly developed two-dimensional wavelets technique has been validated by different illustrative numerical examples to solve two-dimensional Fredholm integral equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations Emerald Publishing

A novel technique based on Bernoulli wavelets for numerical solutions of two-dimensional Fredholm integral equation of second kind

Engineering Computations , Volume 36 (6): 22 – Aug 15, 2019

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Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
0264-4401
DOI
10.1108/ec-11-2018-0500
Publisher site
See Article on Publisher Site

Abstract

A novel technique based on Bernoulli wavelets has been proposed to solve two-dimensional Fredholm integral equation of second kind. Bernoulli wavelets have been created by dilation and translation of Bernoulli polynomials. This paper aims to introduce properties of Bernoulli wavelets and Bernoulli polynomials.Design/methodology/approachTo solve the two-dimensional Fredholm integral equation of second kind, the proposed method has been used to transform the integral equation into a system of algebraic equations.FindingsNumerical experiments shows that the proposed two-dimensional wavelets technique can give high-accurate solutions and good convergence rate.Originality/valueThe efficiency of newly developed two-dimensional wavelets technique has been validated by different illustrative numerical examples to solve two-dimensional Fredholm integral equations.

Journal

Engineering ComputationsEmerald Publishing

Published: Aug 15, 2019

Keywords: Bernoulli wavelets; Two-dimensional Fredholm integral equation; Bernoulli polynomial; Bernoulli numbers; Legendre wavelets; Karhunen–Loéve expansion

References