2013/05/06 by Vı́ctor Domínguez, Dominguez, Victor
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #42A15 #65D30 #65Y20 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1305.1365
openalex publication_date 2013/05/06 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this work we propose and analyse a numerical method for computing a family\nof highly oscillatory integrals with logarithmic singularities. For these\nquadrature rules we derive error estimates in terms of N, the number of\nnodes, k the rate of oscillations and a Sobolev-like regularity of the\nfunction. We prove that that the method is not only robust but the error even\ndecreases, for fixed N, as k increases. Practical issues about the\nimplementation of the rule are also covered in this paper by: (a) writing down\nready-to-implement algorithms; (b) analysing the numerical stability of the\ncomputations and (c) estimating the overall computational cost. We finish by\nshowing some numerical experiments which illustrate the theoretical results\npresented in this paper.\n