Numerical Solution Of Fredholm And Volterra Integral Equations Of The First Kind Using Wavelets Bases

Abstract

The Fredholm and Volterra types of integral equations are appeared in many engineering fields. In this paper, we suggest a method for solving Fredholm and Volterra integral equations of the first kind based on the wavelet bases. The Haar, continuous Legendre, CAS, Chebyshev wavelets of the first kind (CFK) and of the second kind (CSK) are used on [0,1] and are utilized as a basis in Galerkin or collocation method to approximate the solution of the integral equations. In this case, the integral equation converts to the system of linear equations. Then, in some examples the mentioned wavelets are compared with each other.

Some Approximated Solutions For Operator Equations By Using Frames

“…A natural approach to constructing an approximate solution is to solve a finite dimensional analog of the problem (1,1). In [2,6,7,10] some approximated solutions for this equation and related problems has been developed by wavelet bases. Usually the operator under consideration is defined on a bounded domain in ℝ n or on a closed manifold.…”

On Bivariate Haar Functions And Interpolation Polynomial

“…Various wavelet basis are applied, we can see some of wavelet applications in [11][12][13]. One of the wavelet basis is Haar wavelet where we use of this kind of base on Bivariate interpolation polynomial.Before defining the Haar system, we introduce the standard notation for binary intervals, which will be used throughout the rest of the paper.…”