The Euler-Maclaurin Formula in Presence of a Logarithmic Singularity |
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| Authors: | Ricardo Celorrio Francisco-Javier Sayas |
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| Institution: | (1) Departamento Matemática Aplicada-E.U.I.T.I.Z, Universidad de Zaragoza-Corona de Aragón, 50009 Zaragoza, Spain. email: celorrio@posta.unizar.es;(2) Departamento Matemática Aplicada-Centro Politécnico Superior, Universidad de Zaragoza-María de Luna, 3, 50015 Zaragoza, Spain. e-mail: jsayas@posta.unizar.es |
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| Abstract: | In this short note we prove an extension of the Euler-Maclaurin expansion for general rectangular composite quadrature rules in one dimension when the derivative of the integrand has a logarithmic singularity. We show that a correction series has to be added to the formula, but that the asymptotic expansion in powers of the discretization parameter still holds. |
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| Keywords: | Euler-Maclaurin expansions numerical integration |
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