On Volterra integral operators with highly oscillatory kernels

DOI10.3934/dcds.2014.34.915zbMath1278.45016OpenAlexW2083582003MaRDI QIDQ379768

Hermann Brunner

Publication date: 11 November 2013

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2014.34.915

zbMATH Keywords

spectrumcompact operatorsVolterra integral operatorscordial Volterra operatorshighly oscillatory kernelshighly oscillatory solutionsnon-compact Volterra operators

Mathematics Subject Classification ID

Integral operators (45P05) Integral operators (47G10) Volterra integral equations (45D05) Linear integral equations (45A05)

Related Items (16)

Numerical method for solving Volterra integral equations with oscillatory kernels using a transform ⋮ A well-conditioned Levin method for calculation of highly oscillatory integrals and its application ⋮ Meshless procedure for highly oscillatory kernel based one-dimensional Volterra integral equations ⋮ Efficient BBFM-collocation for weakly singular oscillatory Volterra integral equations of the second kind ⋮ Oscillation-preserving Legendre-Galerkin methods for second kind integral equations with highly oscillatory kernels ⋮ An efficient spectral-Galerkin method for second kind weakly singular VIEs with highly oscillatory kernels ⋮ On the convergence rate of collocation methods for Volterra integral equations with weakly singular oscillatory trigonometric kernels ⋮ A collocation boundary value method for linear Volterra integral equations ⋮ The generalized quadrature method for a class of highly oscillatory Volterra integral equations ⋮ Oscillation-free solutions to Volterra integral and integro-differential equations with periodic force terms ⋮ Unnamed Item ⋮ The oscillation of solutions of Volterra integral and integro-differential equations with highly oscillatory kernels ⋮ A Hermite collocation method for approximating a class of highly oscillatory integral equations using new Gaussian radial basis functions ⋮ Frequency-explicit convergence analysis of collocation methods for highly oscillatory Volterra integral equations with weak singularities ⋮ Efficient collocation methods for Volterra integral equations with highly oscillatory kernel ⋮ Hermite-type collocation methods to solve Volterra integral equations with highly oscillatory Bessel kernels

Uses Software

• Eigtool

Cites Work

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