Approximation of functions by Bernoulli wavelet and its applications in solution of Volterra integral equation of second kind

Abstract

In this paper, two new estimators E2k-1,0(1)(f) and E2k-1,M(1)(f) of characteristic function and an estimator E2k-1,M(2)(f) of function of Ho ¨ lder’s class Hα[0 , 1) of order 0 < α⩽ 1 have been established using Bernoulli wavelets. A new technique has been applied for solving Volterra integral equation of second kind using Bernoulli wavelet operational matrix of integration as well as product operational matrix. These matrices have been utilized to reduce the Volterra integral equation into a system of algebraic equations, which are easily solvable. Some examples are illustrated to show the validity and efficiency of proposed technique of this research paper. © 2021, The Author(s).