ﻻ يوجد ملخص باللغة العربية
Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the discretization errors on the frequency parameter of the oscillatory functions show that the accuracy gain of the present formulas over those based on the exponential fitting approach [L. Ixaru, Computer Physics Communications, 105 (1997) 1--19] is overwhelming.
We develop two classes of composite moment-free numerical quadratures for computing highly oscillatory integrals having integrable singularities and stationary points. The first class of the quadrature rules has a polynomial order of convergence and
This work settles the problem of constructing entropy stable non-oscillatory (ESNO) fluxes by framing it as a least square optimization problem. A flux sign stability condition is introduced and utilized to construct arbitrary order entropy stable fl
In this paper, we present a Clenshaw-Curtis-Filon-type method for the weakly singular oscillatory integral with Fourier and Hankel kernels. By interpolating the non-oscillatory and nonsingular part of the integrand at $(N+1)$ Clenshaw-Curtis points,
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the system using an
Prolate spheroidal wave functions provide a natural and effective tool for computing with bandlimited functions defined on an interval. As demonstrated by Slepian et al., the so called generalized prolate spheroidal functions (GPSFs) extend this appa