Numerical methods for multivariate highly oscillatory integrals

ABSTRACT

In this paper, new algorithms are proposed for numerical evaluation of multivariate highly oscillatory integrals having critical point(s) over piecewise smooth rectangular and non-rectangular domains. Multi-resolution analysis is used to take care of the critical point(s). Theoretical error bounds of the component methods of the new algorithms are found. Accuracy of the proposed algorithms is validated numerically on benchmark tests. Numerical results are compared with the methods available in the literature to ascertain stable and accurate performance of the new algorithms.

KEYWORDS:

• Multivariate highly oscillatory integrands
• meshless collocation method
• stationary and resonance point(s)
• hybrid and Haar functions

2010 AMS SUBJECT CLASSIFICATIONS:

• 65GXX
• 65Mxx
• 65Txx
• 65Yxx

Disclosure statement

No potential conflict of interest was reported by the authors.