Extended quadrature rules for oscillatory integrands

DOI10.1016/S0168-9274(03)00009-6zbMath1025.41016OpenAlexW1981373189WikidataQ57778954 ScholiaQ57778954MaRDI QIDQ1399157

Ronald Cools, L. Gr. Ixaru, Kyung Joong Kim

Publication date: 30 July 2003

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(03)00009-6

zbMATH Keywords

quadrature ruleoscillatory integrand

Mathematics Subject Classification ID

Approximate quadratures (41A55)

Related Items (19)

Frequency-dependent interpolation rules using first derivatives for oscillatory functions ⋮ Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday ⋮ Modified Gauss-Laguerre exponential fitting based formulae ⋮ Numerical Integration of Highly Oscillating Functions ⋮ Unnamed Item ⋮ Interpolatory quadrature rules for oscillatory integrals ⋮ Exponentially fitted two-step peer methods for oscillatory problems ⋮ Study the genetic variation using eta functions ⋮ A comparative study of numerical steepest descent, extrapolation, and sequence transformation methods in computing semi-infinite integrals ⋮ On the Levin iterative method for oscillatory integrals ⋮ The least-squares fit of highly oscillatory functions using eta-based functions ⋮ Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval ⋮ Numerical solutions of highly oscillatory integrals ⋮ Error analysis for frequency-dependent interpolation formulas using first derivatives ⋮ Two-frequency-dependent Gauss quadrature rules ⋮ Comparison of Newton-Cotes and Gaussian methods of quadrature ⋮ Exponentially fitted quadrature rules of Gauss type for oscillatory integrands ⋮ Adapted explicit two-step peer methods ⋮ Galerkin-Levin method for highly oscillatory integrals

Uses Software

• EXPFIT4
• Maple

Cites Work

• Unnamed Item
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• EXPFIT4 -- a FORTRAN program for the numerical solution of systems of nonlinear second-order initial-value problems
• Operations on oscillatory functions
• Quadrature rules using first derivatives for oscillatory integrands
• Understanding Maple
• A comment on ``Reliable operations on oscillatory functions
• A Gauss quadrature rule for oscillatory integrands

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