| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4638442 | Journal of Computational and Applied Mathematics | 2015 | 13 Pages |
Abstract
A new interpolatory-type quadrature rule is proposed for the numerical evaluation of Cauchy principal value integrals of oscillatory kind ⨍−11f(x)x−τeiωxdx, where τ∈(−1,1)τ∈(−1,1). The method is based on an interpolatory procedure at Clenshaw–Curtis points and the singular point, and the fast computation of the modified moments with Cauchy type singularity. Based on this result, a new method is presented for the computation of the oscillatory integrals with logarithmic singularities too. These methods enjoy fast implementation and high accuracy. Convergence rates on ωω are also provided. Numerical examples support the theoretical analyses.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Guo He, Shuhuang Xiang,