Abstract
AbstractIn this paper, we will propose the Chebyshev spectral Galerkin and collocation methods for the Fredholm integral equations (fies) of the second kind with smooth kernel and its associated eigenvalue problem (evps). The convergence rates of approximated solutions, iterated solutions with exact solution in \(L^2_\omega \) norm have been investigated. We will evaluate the errors between exact eigen-elements and approximated eigen-elements both in \(L^2_\omega \) and \(L^\infty _\omega \) norms. We will show that eigenvalues and iterated eigenvectors have super-convergence rate in Chebyshev spectral Galerkin methods.KeywordsFredholm integral equationsEigenvalue problemsCompact integral operatorChebyshev polynomials
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