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, e i | u → - v → | 4 π i | u → - 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 ≤ L . We prove that if v = | v → | is large enough, the truncated series gives rise to an error lower than ϵ as soon as L satisfies L + 1 2 ≃ v + C W 2 3 ( K ( α ) ϵ - δ v γ ) v 1 3 where W is the Lambert function, K ( α ) depends only on...

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.