Numerical evaluation of oscillatory-singular integrals

ABSTRACT

In this paper, we consider an asymptotic Filon-type method for computing the oscillatory Cauchy principal value integrals and end-point oscillatory-singular integrals. The method is constructed by using a Lagrange interpolating polynomial to approximate the non-oscillatory function so that it successfully avoids the singularity and solving the systems of equations. Numerical examples and theoretical results show the accuracy and efficiency of the proposed method.

KEYWORDS:

• Singularity
• approximate polynomial
• oscillatory integrals
• numerical evaluation
• error analysis

AMS SUBJECT CLASSIFICATIONS:

• 65D32
• 65D30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by National Social Science Fund of China [grant number 15BJY122] and Natural Science Foundation of Guangdong Province, China [grant number 2015A030313615].