Bernoulli Wavelet Based Numerical Method for Solving Fredholm Integral Equations of the Second Kind

Abstract

In this paper, a Bernoulli wavelet based numerical method for the solution of Fredholm integral equations of the second kind is proposed. The method is based upon Bernoulli wavelet approximations. The Bernoulli wavelet (BW) is first presented and the resulting Bernoulli wavelet matrices are utilized to reduce the Fredholm integral equations into algebraic equations. Solving these equations using MATLAB to obtain Bernoulli coefficients. The numerical results of the proposed method through the illustrative examples is presented in comparison with the exact and existing methods (Haar wavelet method (HWM) [13], Hermite cubic splines (HCS) [11]) of solution from the literature are shown in tables and figures, which show that the validity and applicability of the technique with higher accuracy even for the smaller values of N.