An accelerated Levin–Clenshaw–Curtis method for the evaluation of highly oscillatory integrals

• Published in: BIT Vol. 65; no. 3; p. 36
• Main Authors: Iserles, Arieh, Maierhofer, Georg
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.01.2025; Springer Nature B.V
• Subjects: Chebyshev approximation; Computational Mathematics and Numerical Analysis; Differential equations; Fast Fourier transformations; Fourier transforms; Integrals; Mathematics; Mathematics and Statistics; Numeric Computing; Operators (mathematics); Polynomials; Quadratures; Research Paper; 65D30; Numerical integration; Levin method; Chebyshev polynomials; Highly oscillatory quadrature

The efficient approximation of highly oscillatory integrals plays an important role in a wide range of applications. Whilst traditional quadrature becomes prohibitively expensive in the high-frequency regime, Levin methods provide a way to approximate these integrals in many settings at uniform cost...