Numerical Solution of Fredholm and Volterra Integral Equations of the First Kind Using Wavelets Bases

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Authors
Maryam Bahmanpour
 Department of Mathematics, Sama Technical and Vocational Training College, Islamic Azad University, Khorasgan (Isfahan) Branch, Isfahan, Iran.
Mohammad Ali Fariborzi Araghi
 Department of Mathematics, Central Tehran Branch, Islamic Azad University, P.O.Box 13185.768, Tehran, Iran.
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.
Keywords
 First kind Volterra and Fredholm integral equation
 Galerkin method
 Collocation method
 Haar
 Legendre
 CAS
 CFK
 CSK wavelets.
MSC
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