Deferred correction with mono-implicit Runge-Kutta methods for first-order IVPs
Proceedings of the on Numerical methods for differential equations
Quadrature rules using first derivatives for oscillatory integrands
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Extended quadrature rules for oscillatory integrands
Applied Numerical Mathematics
Stability and Convergence of Collocation Schemes for Retarded Potential Integral Equations
SIAM Journal on Numerical Analysis
Two-frequency-dependent Gauss quadrature rules
Journal of Computational and Applied Mathematics
A Fast Algorithm for the Electromagnetic Scattering from a Large Cavity
SIAM Journal on Scientific Computing
On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
SIAM Journal on Numerical Analysis
Truncation Errors in Exponential Fitting for Oscillatory Problems
SIAM Journal on Numerical Analysis
A Sparse Discretization for Integral Equation Formulations of High Frequency Scattering Problems
SIAM Journal on Scientific Computing
Exponentially fitted quadrature rules of Gauss type for oscillatory integrands
Applied Numerical Mathematics
On modified Mellin transforms, Gauss-Laguerre quadrature, and the valuation of American call options
Journal of Computational and Applied Mathematics
Exponential fitting Direct Quadrature methods for Volterra integral equations
Numerical Algorithms
Mathematics and Computers in Simulation
Exponentially fitted two-step hybrid methods for y″=f(x,y)
Journal of Computational and Applied Mathematics
Numerical approximations to integrals with a highly oscillatory Bessel kernel
Applied Numerical Mathematics
Applied Numerical Mathematics
Hi-index | 7.29 |
New quadrature formulae are introduced for the computation of integrals over the whole positive semiaxis when the integrand has an oscillatory behaviour with decaying envelope. The new formulae are derived by exponential fitting, and they represent a generalization of the usual Gauss-Laguerre formulae. Their weights and nodes depend on the frequency of oscillation in the integrand, and thus the accuracy is massively increased. Rules with one up to six nodes are treated with details. Numerical illustrations are also presented.