Filon-Clenshaw-Curtis rules for a class of highly-oscillatory integrals with logarithmic singularities

• Autores: Víctor Domínguez Báguena
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 261, Nº 1, 2014, págs. 299-319
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.11.012
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• Resumen

  • In this work we propose and analyse a numerical method for computing a family of highly oscillatory integrals with logarithmic singularities. For these quadrature rules we derive error estimates in terms of N, the number of nodes, k the rate of oscillations and a Sobolevlike regularity of the function. We prove that the method is not only robust but the error even decreases, for fixed N, as k increases. Practical issues about the implementation of the rule are also covered in this paper by: (a) writing down ready-to-implement algorithms;

    (b) analysing the numerical stability of the computations and (c) estimating the overall computational cost. We finish by showing some numerical experiments which illustrate the theoretical results presented in this paper.