On the Convolution Quadrature Rule for Integral Transforms with Oscillatory Bessel Kernels

Ma, Junjie; Liu, Huilan

doi:10.3390/sym10070239

Cited by 10 publications

(3 citation statements)

References 32 publications

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“…where the 𝑤 < ′𝑠 are the weights and the 𝑝 < ′𝑠 are the integration points. To apply the rule over an arbitrary interval [𝑎, 𝑏], we use the change of variable [10]- [ 12]…”

Section: The Radial Kernel Collocation Methodsmentioning

confidence: 99%

A Numerical Method for Fredholm Integro-Differential Equation using Positive Definite Radial Kernels and A Study of the Effect of The Shape Parameter

Nengem,

Aboiyar,

Swem

et al. 2023

EJMATH

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In this paper, we use two radial kernels, the Generalized Multiquadrics and the linear Laguerre-Gaussians for the formulation of radial kernel collocation method for solving problems involving Fredholm integro-differential equations. The effect of the shape parameter contained in each of the kernels, on the accuracy of the method is investigated. The method is demonstrated using two examples the numerical results displayed in form of tables and graphs. MATLAB 2018a was used for the implementation.

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Section: The Radial Kernel Collocation Methodsmentioning

confidence: 99%

A Numerical Method for Fredholm Integro-Differential Equation using Positive Definite Radial Kernels and A Study of the Effect of The Shape Parameter

Nengem,

Aboiyar,

Swem

et al. 2023

EJMATH

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“…The coefficients ω j (h) can be calculated numerically, taking z = ρe iθ in (29) and applying the composite trapezoidal rule to 2π-periodic function θ → Q h −1 δ(ρe iθ ) e −i jθ in M points, An alternative method for calculating quadrature weights ω j (h) can be done in the following form (cf. [3], [9], [20])…”

Section: Convolution Quadrature Methodsmentioning

confidence: 99%

Calculation of the channel discharge function for the generalized lightning traveling current source return stroke model

Pavlović¹,

Milovanović²,

Cvetić³

2018

Filomat

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The generalized lightning traveling current source return stroke model (also called GTCS model) represents generalization of all engineering lightning return stroke models that is generalization of the transmission line (TL models, also called current propagation models) and traveling current source models (TCS models, also known as current generation models). The channel discharge function was introduced and calculated for special cases within the GTCS model. We applied new numerical method for the calculation of the channel discharge function. The proposed method is highly accurate, extremely efficient and relatively simple.

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“…In recent years, there has been tremendous interest in developing methods for solving highly oscillatory Volterra integral equation, such as discontinuous Galerkin method [5], Filon-type method [6,7], collocation method [4,8,9], collocation boundary value method [10,11], collocation method on uniform mesh [12], collocation method on graded mesh [13].…”

Section: Introductionmentioning

confidence: 99%

Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels

Fang

Xiang

2019

Symmetry

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In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods.

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On the Convolution Quadrature Rule for Integral Transforms with Oscillatory Bessel Kernels

Cited by 10 publications

References 32 publications

A Numerical Method for Fredholm Integro-Differential Equation using Positive Definite Radial Kernels and A Study of the Effect of The Shape Parameter

A Numerical Method for Fredholm Integro-Differential Equation using Positive Definite Radial Kernels and A Study of the Effect of The Shape Parameter

Calculation of the channel discharge function for the generalized lightning traveling current source return stroke model

Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels

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