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

Volume 5, Issue 4, pp 337-345 http://dx.doi.org/10.22436/jmcs.05.04.12

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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.

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Keywords

• First kind Volterra and Fredholm integral equation
• Galerkin method
• Collocation method
• Haar
• Legendre
• CAS
• CFK
• CSK wavelets.

MSC

•  45B05
•  65R20
•  45D05
•  65T60

References

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