The oscillation of solutions of Volterra integral and integro-differential equations with highly oscillatory kernels

DOI10.1216/JIE-2015-27-4-455zbMath1381.45009MaRDI QIDQ5963117

Yunyun Ma, Yuesheng Xu, Hermann Brunner

Publication date: 4 March 2016

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jiea/1454939250

zbMATH Keywords

Volterra integral equationdecomposition of the oscillatory integralhighly oscillatory kerneloscillation preserving solutionoscillatory structured spaceVolterra integro-differential equation

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Volterra integral equations (45D05) Integral equations with miscellaneous special kernels (45H05)

Related Items

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 ⋮ Oscillation-free solutions to Volterra integral and integro-differential equations with periodic force terms ⋮ Meshless methods for two-dimensional oscillatory Fredholm integral equations ⋮ Volterra integral equations with highly oscillatory kernels: a new numerical method with applications ⋮ 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 ⋮ Meshless approximation method of one-dimensional oscillatory Fredholm integral equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Volterra integral operators with highly oscillatory kernels
• Analysis of a collocation method for integrating rapidly oscillatory functions
• Efficient Filon-type methods for \(\int_a^b f(x)\,e^{i\omega g(x)}\, dx\)
• A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations
• Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels
• Identification problems of wave phenomena. Theory and numerics
• Fast, numerically stable computation of oscillatory integrals with stationary points
• The computation of the spectra of highly oscillatory Fredholm integral operators
• Filon--Clenshaw--Curtis Rules for Highly Oscillatory Integrals with Algebraic Singularities and Stationary Points
• Asymptotic expansion and Filon-type methods for a Volterra integral equation with a highly oscillatory kernel
• Stability and error estimates for Filon-Clenshaw-Curtis rules for highly oscillatory integrals
• Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications
• On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
• The Construction of cubature rules for multivariate highly oscillatory integrals
• The Formula of FAA Di Bruno
• Procedures for Computing One- and Two-Dimensional Integrals of Functions with Rapid Irregular Oscillations
• The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
• The Curious History of Faa di Bruno's Formula
• Computing highly oscillatory integrals
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• The spectral problem for a class of highly oscillatory Fredholm integral operators
• Efficient quadrature of highly oscillatory integrals using derivatives
• Moment-free numerical integration of highly oscillatory functions
• Quadrature methods for multivariate highly oscillatory integrals using derivatives
• Integral Equations with a Rapidly Oscillating Kernel

This page was built for publication: The oscillation of solutions of Volterra integral and integro-differential equations with highly oscillatory kernels