On the computation of Riccati-Bessel functions

Peter Maličký; Marianna Maličká

Displaying similar documents to “On the computation of Riccati-Bessel functions”

Error estimates in the fast multipole method for scattering problems. Part 2 : truncation of the Gegenbauer series

Quentin Carayol, Francis Collino (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We perform a complete study of the truncation error of the Gegenbauer series. This series yields an expansion of the Green kernel of the Helmholtz equation, $\frac{e^{i | \vec{u} - \vec{v} |}}{4 π i | \vec{u} - \vec{v} |}$ , which is the core of the Fast Multipole Method for the integral equations. We consider the truncated series where the summation is performed over the indices $ℓ \leq L$ . We prove that if $v = | \vec{v} |$ is large enough, the truncated series gives rise to an error lower than $ϵ$ as soon as $L$ satisfies $L + \frac{1}{2} ≃ v + C W^{\frac{2}{3}} (K (α) ϵ^{- δ} v^{γ}) v^{\frac{1}{3}}$ where $W$ is the Lambert function, $K (α)$ depends only on...

Algorithms. 18. Algorithmus for evaluation of spherical Bessel functions

Jozef Zelenka (1969)

Aplikace matematiky

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On the computation of Aden functions

Peter Maličký, Marianna Maličká (1991)

Applications of Mathematics

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The paper deals with the computation of Aden functions. It gives estimates of errors for the computation of Aden functions by downward reccurence.

Monte Carlo modelling of the radiation transport in polydispersion media

M. Šolc (1980)

Acta Universitatis Carolinae. Mathematica et Physica

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Numerical study of the systematic error in Monte Carlo schemes for semiconductors

Orazio Muscato, Wolfgang Wagner, Vincenza Di Stefano (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The paper studies the convergence behavior of Monte Carlo schemes for semiconductors. A detailed analysis of the systematic error with respect to numerical parameters is performed. Different sources of systematic error are pointed out and illustrated in a spatially one-dimensional test case. The error with respect to the number of simulation particles occurs during the calculation of the internal electric field. The time step error, which is related to the splitting of transport and electric...

Backward recurrence relations for Bennett functions

Sternberg, Robert L., Sternberg, Helen M. (1976)

Portugaliae mathematica

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Error estimates in the fast multipole method for scattering problems. Part 1 : truncation of the Jacobi-Anger series

Quentin Carayol, Francis Collino (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We perform a complete study of the truncation error of the Jacobi-Anger series. This series expands every plane wave $e^{i \hat{s} \cdot \vec{v}}$ in terms of spherical harmonics ${Y_{ℓ, m} (\hat{s})}_{| m | \leq ℓ \leq \infty}$ . We consider the truncated series where the summation is performed over the $(ℓ, m)$ ’s satisfying $| m | \leq ℓ \leq L$ . We prove that if $v = | \vec{v} |$ is large enough, the truncated series gives rise to an error lower than $ϵ$ as soon as $L$ satisfies $L + \frac{1}{2} ≃ v + C W^{\frac{2}{3}} (K ϵ^{- δ} v^{γ}) v^{\frac{1}{3}}$ where $W$ is the Lambert function and $C, K, δ, γ$ are pure positive constants. Numerical experiments show that this asymptotic is optimal....