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

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.