The abstract nonlocal boundary value problem −d2u t /dt2 Au t g t , 0 < t < 1, du t /dt − Au t f t , 1 < t < 0, u 1 u −1 μ for differential equations in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in Hölder spaces with a weight is established. The coercivity inequalities for the solution of boundary value problems for el...

The present work is concerned with the development of commutative discrete filters for unstructured grids and contains two main contributions. First, building on the work of Marsden et al. [J. Comp. Phys. 175 (2002) 584], a new commutative discrete filter based on least-squares techniques is constructed. Second, a new analysis of the discrete commutation error is carried out. The analysis indic...

Discontinuous Galerkin methods are developed for solving the Vlasov–Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov–Maxwell system. The proposed scheme employs discontinuous Galerki...

The distributions of the largest and the smallest eigenvalues of a p-variate sample covariance matrix S are of great importance in statistics. Focusing on the null case where nS follows the standard Wishart distribution Wp(I, n), we study the accuracy of their scaling limits under the setting: n/p → γ ∈ (0,∞) as n → ∞. The limits here are the orthogonal Tracy-Widom law and its reflection about ...

A hardly known and very important result of Kreiss is proven explicitly: Outflow boundary extrapolation, which complements stable dissipative schemes for linear hyperbolic initial value problems, maintains stability. In view of this result, the Lax-Wendroff and the Gottlieb-Turkel schemes are applied to a test problem. As expected from the rate-of-convergence theory by Gustafsson, global order ...

In this paper an analysis of the global AAM conservation properties of NCAR’s Community Atmosphere Model Spectral Element (CAM-SE) dynamical core under HeldSuarez forcing is presented. It is shown that the spurious sources/sinks of AAM in CAMSE are three orders of magnitude smaller than the parameterized (physical) sources/sinks. The effect on AAM conservation by changing various numerical aspe...

A definition of even and odd matrices is given, and some of their elementary properties stated. The basic result is that if λ is an eigenvalue of an odd matrix, then so is −λ. Starting from this, there is a consideration of some ways of using odd matrices to test the order of accuracy of eigenvalue routines. 1. Definitions and some elementary properties Let us call a matrix W even if its elemen...

The minimized dispersion and controllable dissipation (MDCD) reconstruction technique optimizes dispersion and dissipation separately and shows desirable properties of both dispersion and dissipation. A low dispersion finite volume scheme based on MDCD reconstruction is proposed which is capable of handling flow discontinuities and resolving a broad range of length scales. Although the proposed...

—For a randomized stochastic optimization algorithm, consistency conditions of estimates are slackened and the order of accuracy for a finite number of observations is studied. A new method of realization of this algorithm on quantum computers is developed.