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

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.