Numerical expansion methods for solving integral equations by interpolation and Gauss quadrature rules

摘要

In this paper, we introduce a numerical method for solving linear integral equations. The main idea based on interpolation for unknown function, where is interpolated in the zeros of the Chebyshev’s polynomials. Next, we use Gauss quadrature rules as Gauss–Chebyshev or Clenshaw–Curtis. The technique is very effective and simple, specially, for integral equations of first kind, as Fredholm’s and Volterra’s types. In the end, for showing efficiency of this method, we use numerical examples.