## Journal of Applied Mathematics

### The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels

Qinghua Wu

#### Abstract

A method for approximating the solution of weakly singular Fredholm integral equation of the second kind with highly oscillatory trigonometric kernel is presented. The unknown function is approximated by expansion of Chebychev polynomial and the coefficients are determinated by classical collocation method. Due to the highly oscillatory kernels of integral equation, the discretised collocation equation will give rise to the computation of oscillatory integrals. These integrals are calculated by using recursion formula derived from the fundamental recurrence relation of Chebyshev polynomial. The effectiveness and accuracy of the proposed method are tested by numerical examples.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 172327, 7 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305692

Digital Object Identifier
doi:10.1155/2014/172327

Mathematical Reviews number (MathSciNet)
MR3198361

#### Citation

Wu, Qinghua. The Approximate Solution of Fredholm Integral Equations with Oscillatory Trigonometric Kernels. J. Appl. Math. 2014 (2014), Article ID 172327, 7 pages. doi:10.1155/2014/172327. https://projecteuclid.org/euclid.jam/1425305692

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