Abstract
Calculation of highly oscillatory integrals is a challenging and everlasting topic in computational mathematics. Levin-type methods provide well-behaved solutions for this problem, since they are free of computing moments compared to Filon-type methods. However, numerical treatments of related ordinary differential equations add complexities. In this paper, based on the fast computation of barycentric weights of Hermite interplant, a class of differential matrices are derived and applied to implementing Levin-type methods. Furthermore, a modified delaminating quadrature rule for multivariate integrals with oscillatory kernels is also developed. Numerical experiments show their effectiveness in calculating highly oscillatory integrals.
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