A novel technique based on Bernoulli wavelets for numerical solutions of two-dimensional Fredholm integral equation of second kind. Issue 6 (8th July 2019)

• Record Type: Journal Article
• Authors: Saha Ray, S.; Behera, S.
• Is Part Of: Engineering computations. Volume 36:Issue 6(2019)
• Page Start: 1798
• Page End: 1819
• Publication Date: 2019-07-08
• Subjects: Bernoulli wavelets -- Two-dimensional Fredholm integral equation -- Bernoulli polynomial -- Bernoulli numbers -- Legendre wavelets -- Karhunen–Loéve expansion; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-11-2018-0500
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: 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/approach: To 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. Findings: Numerical experiments shows that the proposed two-dimensional wavelets technique can give high-accurate solutions and good convergence rate. Originality/value: The efficiency of newly developed two-dimensional wavelets technique has been validated by different illustrative numerical examples to solve two-dimensional Fredholm integral equations.