Extended Bernoulli wavelet approximation method and its applications in solving Lane-Emdane differential equation and linear integral equation

Abstract

In this paper, we generalized the Bernoulli wavelet called extended Bernoulli wavelets (EBWs). The EBWs are derived by dilation and translation of the Bernoulli polynomials. We solved Lane-Emdane differential equation with the help of extended Bernoulli wavelet method and compared proposed method with Legendre wavelet method, Chebyshev wavelet method (first kind and
second kind) and Gegenbauer wavelet method. Also, we solved linear integral equation with the help of proposed method and compared with Legendre wavelet method. Illustrative examples have been discussed to demonstrate the validity and applicability of the present method.