|Title:||Fast computation of Goursat’s infinite integral with very high accuracy|
|Author's alias:||大浦, 拓哉|
Double exponential quadrature method
|Journal title:||Journal of Computational and Applied Mathematics|
|Abstract:||We propose an efficient computation method for the infinite integral View the MathML source, whose integrand contains a series of spikes, approximately π apart, growing taller and narrower as x increases. Computing the value of this integral has been a problem since 1984. We herein demonstrate a method using the Hilbert transform for changing this type of singular function into a smooth function and computing the value of the integral to more than one million significant digits using a superconvergent double exponential quadrature method.|
|Rights:||© 2013 Elsevier B.V.|
This is not the published version. Please cite only the published version.
|Appears in Collections:||Journal Articles|
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