A comparison of some methods for the evaluation of highly oscillatory integrals
From MaRDI portal
Publication:1964076
DOI10.1016/S0377-0427(99)00213-7zbMath0947.65148MaRDI QIDQ1964076
Publication date: 2 November 2000
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Numerical methods for trigonometric approximation and interpolation (65T40) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)
Related Items
Efficient quadrature for highly oscillatory integrals involving critical points ⋮ Option pricing with Legendre polynomials ⋮ Filon-Clenshaw-Curtis formulas for highly oscillatory integrals in the presence of stationary points ⋮ Evaluation of Cauchy principal value integrals of oscillatory kind ⋮ An \(\mathcal O(1)\) integration scheme for three-dimensional surface scattering problems ⋮ On the effectiveness of spectral methods for the numerical solution of multi-frequency highly oscillatory Hamiltonian problems ⋮ Interpolatory quadrature rules for oscillatory integrals ⋮ A rapid solution of a kind of 1D Fredholm oscillatory integral equation ⋮ Efficient Filon method for oscillatory integrals ⋮ Asymptotically derived boundary elements for the Helmholtz equation in high frequencies ⋮ Superinterpolation in highly oscillatory quadrature ⋮ Quadrature formulae of many highly oscillatory Fourier-type integrals with algebraic or logarithmic singularities and their error analysis ⋮ Energy conservation issues in the numerical solution of the semilinear wave equation ⋮ Numerical approximation of oscillatory integrals of the linear ship wave theory ⋮ A universal solution to one-dimensional oscillatory integrals ⋮ Method for numerical integration of rapidly oscillating functions in diffraction theory ⋮ On an improved-Levin oscillatory quadrature method ⋮ Two-frequency-dependent Gauss quadrature rules ⋮ A note on a recent study of oscillatory integration rules ⋮ Error bounds for approximation in Chebyshev points ⋮ Shifted GMRES for oscillatory integrals ⋮ Quadrature rules for the integration of the product of two oscillatory functions with different frequencies ⋮ Exponentially fitted quadrature rules of Gauss type for oscillatory integrands ⋮ An improved Levin quadrature method for highly oscillatory integrals ⋮ The discontinuous enrichment method ⋮ Exact integration of polynomial-exponential products with application to wave-based numerical methods ⋮ Delaminating quadrature method for multi-dimensional highly oscillatory integrals ⋮ Exact integration scheme for planewave-enriched partition of unity finite element method to solve the Helmholtz problem ⋮ Development of 3D PUFEM with linear tetrahedral elements for the simulation of acoustic waves in enclosed cavities ⋮ Integrating oscillatory functions in M<scp>atlab</scp> ⋮ Uniform approximations to Cauchy principal value integrals of oscillatory functions ⋮ Numerical results for Saito’s uniqueness theorem in inverse scattering theory ⋮ Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function ⋮ Quadrature rules using first derivatives for oscillatory integrands
Cites Work
- A high order, progressive method for the evaluation of irregular oscillatory integrals
- Product integration with the Clenshaw-Curtis points: Implementation and error estimates
- A method for numerical integration on an automatic computer
- A three-point formula for numerical quadrature of oscillatory integrals with variable frequency
- On high precision methods for the evaluation of Fourier integrals with finite and infinite limits
- Product-integration with the Clenshaw-Curtis and related points: Convergence properties
- A note on the numerical solution of linear recurrence relations
- Two robust methods for irregular oscillatory integrals over a finite range
- Indefinite integration of oscillatory functions by the Chebyshev series expansion
- An expansion method for irregular oscillatory integrals
- Product Integration Rules at Clenshaw-Curtis and Related Points: A Robust Implementation
- Product-Integration Rules Based on the Zeros of Jacobi Polynomials
- Procedures for Computing One- and Two-Dimensional Integrals of Functions with Rapid Irregular Oscillations
- Automatic generation of quadrature formulae for oscillatory integrals
- Numerical Evaluation of Fourier Integrals
- The use of Chebyshev series for the evaluation of oscillatory integrals
- Error Estimation in the Clenshaw-Curtis Quadrature Formula
- Numerical solution of second-order linear difference equations
- A Simple "Filon-Trapezoidal" Rule
- A numerical method for the integration of oscillatory functions
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item