Paper Info
Title
Asymptotic error expansions and splitting extrapolation algorithm for two classes of two-dimensional Cauchy principal-value integrals.
Abstract
This paper proposes numerical quadrature rules for two-dimensional Cauchy principal-value integrals of the forms ∫∫Ωf(x,y)(x−s)2+(y−t)2dydx and ∫∫Ωf(x,y)(x−s)(y−t)dydx. The derivation of these quadrature rules is based on the Euler–Maclaurin error expansion of a modified trapezoidal rule for one-dimensional Cauchy singular integrals. The corresponding error estimations are investigated, and the convergence rates O(hm2μ+hn2μ) are obtained for the proposed quadrature rules, where hm and hn are partition sizes in x and y directions, μ is a positive integer determined by integrand. To further improve accuracy, a splitting extrapolation algorithm is developed based on the asymptotic error expansions. Several numerical tests are performed to verify the effectiveness of the proposed methods.
Year
DOI
Venue
2019
10.1016/j.amc.2019.03.056
Applied Mathematics and Computation
Keywords
Field
DocType
Two-dimensional Cauchy principal-value integral,Asymptotic error expansion,Quadrature rule,Splitting extrapolation algorithm
Singular integral,Mathematical analysis,Numerical integration,Trapezoidal rule,Algorithm,Cauchy distribution,Extrapolation,Quadrature (mathematics),Partition (number theory),Cauchy principal value,Mathematics
Journal
Volume
ISSN
Citations 
357
0096-3003
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Yanying Ma100.68
Jin Huang22910.71