Numerical approximations of highly oscillatory Hilbert transforms
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DOI: 10.1007/s40314-020-01193-9
Abstract: In this paper, we are concerned with the numerical approximations of one-sided Hilbert transforms with oscillatory kernel by means of the multiple integrals. This type of Hilbert transform has two computing difficulties: singularity and oscillation.… read more here.
Keywords: hilbert transforms; highly oscillatory; oscillatory hilbert; hilbert ... See more keywords
Filon–Clenshaw–Curtis formulas for highly oscillatory integrals in the presence of stationary points
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DOI: 10.1016/j.apnum.2017.02.003
Abstract: Abstract Numerical approximation of a general class of one-dimensional highly oscillatory integrals over bounded intervals with exponential oscillators is considered. A Filon-type method based on modified Clenshaw–Curtis quadrature rules is developed and its stability is… read more here.
Keywords: filon clenshaw; stationary points; oscillatory integrals; highly oscillatory ... See more keywords
Frequency-explicit convergence analysis of collocation methods for highly oscillatory Volterra integral equations with weak singularities
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DOI: 10.1016/j.apnum.2019.12.013
Abstract: Abstract Filon collocation methods are well known for their good performances in solving the second-kind highly oscillatory Volterra integral equations with weak singularities. As the frequency increases, these methods can provide much more accurate solutions… read more here.
Keywords: frequency; highly oscillatory; collocation methods; volterra integral ... See more keywords
Effective collocation methods to solve Volterra integral equations with weakly singular highly oscillatory Fourier or Airy kernels
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DOI: 10.1080/00207160.2023.2203786
Abstract: In this paper two collocation methods, the direct linear interpolation collocation method and the direct high order interpolation collocation method, are proposed to solve the second kind of Volterra integral equations with weakly singular highly… read more here.
Keywords: highly oscillatory; collocation methods; interpolation collocation; collocation ... See more keywords