Frequency-explicit convergence analysis of collocation methods for highly oscillatory Volterra integral equations with weak singularities

DOI10.1016/j.apnum.2019.12.013zbMath1439.65227OpenAlexW2996470326WikidataQ126535848 ScholiaQ126535848MaRDI QIDQ2301380

Junjie Ma, Hongchao Kang

Publication date: 24 February 2020

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2019.12.013

zbMATH Keywords

Volterra integral equationconvergence ratehighly oscillatory integralweakly singularFilon collocation method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Asymptotics of solutions to integral equations (45M05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Volterra integral equations (45D05)

Related Items (1)

Effective collocation methods to solve Volterra integral equations with weakly singular highly oscillatory Fourier or Airy kernels

Uses Software

• DLMF

Cites Work

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• On Volterra integral operators with highly oscillatory kernels
• Asymptotic stability of solutions to Volterra-renewal integral equations with space maps
• On Filon methods for a class of Volterra integral equations with highly oscillatory Bessel kernels
• Note on the homotopy perturbation method for multivariate vector-value oscillatory integrals
• Numerical solutions to Volterra integral equations of the second kind with oscillatory trigonometric kernels
• A well-conditioned Levin method for calculation of highly oscillatory integrals and its application
• Laplace transforms for approximation of highly oscillatory Volterra integral equations of the first kind
• A collocation boundary value method for linear Volterra integral equations
• Oscillation-free solutions to Volterra integral and integro-differential equations with periodic force terms
• Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels
• Laplace transforms for evaluation of Volterra integral equation of the first kind with highly oscillatory kernel
• On the convergence rates of Filon methods for the solution of a Volterra integral equation with a highly oscillatory Bessel kernel
• Quadrature rules and asymptotic expansions for two classes of oscillatory Bessel integrals with singularities of algebraic or logarithmic type
• Modified asymptotic orders of the direct Filon method for a class of Volterra integral equations
• Stress obtained by interpolation methods for a boundary value problem in linear viscoelasticity
• An electromagnetic inverse problem for dispersive media
• On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
• Fast integration of highly oscillatory integrals with exotic oscillators
• Procedures for Computing One- and Two-Dimensional Integrals of Functions with Rapid Irregular Oscillations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• On the numerical quadrature of highly-oscillating integrals I: Fourier transforms
• The oscillation of solutions of Volterra integral and integro-differential equations with highly oscillatory kernels

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