On the Levin iterative method for oscillatory integrals
نویسندگان
چکیده
منابع مشابه
TWO LOW-ORDER METHODS FOR THE NUMERICAL EVALUATION OF CAUCHY PRINCIPAL VSlLUE INTEGRALS OF OSCILLATORY KIND
In this paper, we develop two piecewise polynomial methods for the numerical evaluation of Cauchy Principal Value integrals of oscillatory kind. The two piecewisepolynomial quadratures are compact, easy to implement, and are numerically stable. Two numerical examples are presented to illustrate the two rules developed, The convergence of the two schemes is proved and some error bounds obtai...
متن کاملA User-Friendly Extrapolation Method for Oscillatory Infinite Integrals
In a recent publication [4] the author developed an extrapolation method, the ^-transformation, for the accurate computation of convergent oscillatory infinite integrals. In yet another publication [6] this method was shown to be applicable to divergent oscillatory infinite integrals that are defined in the sense of summability. The application of the VK-transformation involves some asymptotic ...
متن کاملHomogeneous Estimates for Oscillatory Integrals
Abstract. Let u(x, t) be the solution to the free time-dependent Schrödinger equation at the point (x, t) in space-time Rn+1 with initial data f . We characterize the size of u in terms Lp(Lq)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces Ḣs (Rn). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interp...
متن کاملShifted GMRES for oscillatory integrals
None of the existing methods for computing the oscillatory integral ∫ b a f(x)e iωg(x) dx achieve all of the following properties: high asymptotic order, stability, avoiding deformation into the complex plane and insensitivity to oscillations in f . We present a new method that satisfies these properties, based on applying the gmres algorithm to a shifted linear differential operator.
متن کاملPreconditioned GMRES for oscillatory integrals
None of the existing methods for computing the oscillatory integral ∫ b a f(x)e iωg(x) dx achieve all of the following properties: high asymptotic order, stability, avoiding the computation of the path of steepest descent and insensitivity to oscillations in f . We present a new method that satisfies these properties, based on applying the gmres algorithm to a preconditioned differential operator.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2008
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.06.012