In this paper, we first address the space-time decay properties for higher-order derivatives of strong solutions to the Boussinesq system in the usual Sobolev space. The decay rates obtained here are optimal. The proo...
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In this paper, we first address the space-time decay properties for higher-order derivatives of strong solutions to the Boussinesq system in the usual Sobolev space. The decay rates obtained here are optimal. The proof is based on a parabolic interpolation inequality, bootstrap argument, and some weighted estimates. Secondly, we present a new solution integration formula for the Boussinesq system, which will be employed to establish the existence of strong solutions for small initial data in some scaling invariant function spaces. The smallness conditions are somehow weaker than those presented by Brandolese and Schonbek. We further investigate the asymptotic profiles and decay properties of these strong solutions. Copyright (C) 2016 John Wiley & Sons, Ltd.
Bstj 46: 6. July-August 1967: Two Theorems on the Accuracy of Numerical Solutions of Systems of Ordinary Differential Equations. (Sandberg, I.W.) by published by
Bstj 46: 6. July-August 1967: Two Theorems on the Accuracy of Numerical Solutions of Systems of Ordinary Differential Equations. (Sandberg, I.W.) by published by
A fourth degree integration formula is given for the n-dimensional simplex for all n >= 2, which is invariant under the group G of all affine transformations of T(n) onto itself. The formula contains (n(2) + 5n + 6...
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A fourth degree integration formula is given for the n-dimensional simplex for all n >= 2, which is invariant under the group G of all affine transformations of T(n) onto itself. The formula contains (n(2) + 5n + 6)/2 nodes. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.
We propose a numerical method to approximate a given continuous distribution by a discrete distribution with prescribed moments. The approximation is achieved by minimizing the Kullback-Leibler information of the unkn...
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We propose a numerical method to approximate a given continuous distribution by a discrete distribution with prescribed moments. The approximation is achieved by minimizing the Kullback-Leibler information of the unknown discrete distribution relative to the known continuous distribution (evaluated at given discrete points) subject to some moment constraints. We study the theoretical error bound and the convergence property of the method. The order of the theoretical error bound of the expectation of any bounded measurable function with respect to the approximating discrete distribution is never worse than the integration formula we start with, and therefore the approximating discrete distribution weakly converges to the given continuous distribution. Moreover, we present some numerical examples that show the advantage of our method. [ABSTRACT FROM AUTHOR]
We give a generalization of random matrix ensembles, which includes all classical ensembles. We derive the joint-density function of the generalized ensemble by one simple formula, giving a direct and unified way to c...
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We give a generalization of random matrix ensembles, which includes all classical ensembles. We derive the joint-density function of the generalized ensemble by one simple formula, giving a direct and unified way to compute the density functions for all classical ensembles and various kinds of new ensembles. An integration formula associated with the generalized ensembles is given. We propose a taxonomy of generalized ensembles encompassing all classical ensembles and some new ones not considered before.
We construct two-frequency-dependent Gauss quadrature rules which can be applied for approximating the integration of the product of two oscillatory functions with different frequencies beta(1) and beta(2) of the form...
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We construct two-frequency-dependent Gauss quadrature rules which can be applied for approximating the integration of the product of two oscillatory functions with different frequencies beta(1) and beta(2) of the forms, y(i)(x) = f(i,1)(x) cos(beta(i)x) + f(1,2)(x) Sin (beta(i)x), i = 1, 2, where the functions f(i,j)(x) are smooth. A regularization procedure is presented to avoid the singularity of the Jacobian matrix of nonlinear system of equations which is induced as one frequency approaches the other frequency. We provide numerical results to compare the accuracy of the classical Gauss rule and one- and two-frequency-dependent rules. (C) 2004 Elsevier B.V. All rights reserved.
We construct quadrature rules for the efficient computation of the integral of a product of two oscillatory functions y(1)(x) and y(2)(x), where y(i)(x) = f(i,1) (x) cos (beta(i)x) + f(i,2) (x) sin (beta(i)x), i = 1, ...
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We construct quadrature rules for the efficient computation of the integral of a product of two oscillatory functions y(1)(x) and y(2)(x), where y(i)(x) = f(i,1) (x) cos (beta(i)x) + f(i,2) (x) sin (beta(i)x), i = 1, 2, and the functions f(i,j) (x) are smooth. The weights are evaluated by the exponential fitting technique of Ixaru [Comput. Phys. Comm. 105 (1997) 1-19], which is now extended to cover the case of two frequencies. We give a numerical illustration on how the new rules compare for accuracy with the one-frequency dependent rules and with the classical ones. (C) 2003 Elsevier Science B.V. All rights reserved.
We consider the integral of a function gamma(x), I[y] = integral(-1)(1) y(x) dx and its approximation by a quadrature rule of the form [GRAPHICS] i.e., by a rule which uses the values of both gamma and its derivatives...
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We consider the integral of a function gamma(x), I[y] = integral(-1)(1) y(x) dx and its approximation by a quadrature rule of the form [GRAPHICS] i.e., by a rule which uses the values of both gamma and its derivatives up to p-th order at the nodes of the quadrature rule. We focus only on the case when the nodes are assumed known and present the procedure to calculate the weights. Two cases are actually examined: (i) y(x) is a polynomial and (ii) y(x) is an omega dependent function of the form y(x) = f(1) (x) sin(omegax) + f(2)(x) cos(omegax) with smoothly varying f(1) and f(2). For the latter case, the weights omega(k)((j)) (j = 0, 1,..., p) are omega dependent. A series of specific properties for this case is established and a numerical illustration is given. (C) 2003 IMACS. Published by Elsevier Science B.V All rights reserved.
We consider the integral of a function y(x), I(y(x)) =x integral(-1)(1) y(x) dx and its approximation by a quadrature rule of the form Q(N)(y(x)) =Sigma(k=1)(N) Wky(x(h)) +Sigma(k=1)(N) alphaky'(x(h)) i.e., by a r...
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We consider the integral of a function y(x), I(y(x)) =x integral(-1)(1) y(x) dx and its approximation by a quadrature rule of the form Q(N)(y(x)) =Sigma(k=1)(N) Wky(x(h)) +Sigma(k=1)(N) alphaky'(x(h)) i.e., by a rule which uses the values of both y and its derivative at nodes of the quadrature rule. We examine the cases when the integrand is either a smooth function or an omega dependent function of the form y(x) = f(1)(x) sin(omegax) + f(2)(x) cos(omegax) with smoothly varying f1 and f2. In the latter case, the weights w(lambda) and alpha(k) are omega dependent. We establish some general properties of the weights and present some numerical illustrations. (C) 2002 Elsevier Science B.V. All rights reserved.
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