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Numerical integration of the Cartesian equations of motion of a system with constraints: molecular dynamics of nalkanes
 J. Comput. Phys
, 1977
"... A numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated. The relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration. The method ..."
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Cited by 704 (6 self)
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A numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated. The relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration. The method
Numerical Integration
 In Encyclopedia of Biostatistics
, 1997
"... This article describes classical quadrature methods and, more briefly, some of the more advanced methods for which software is widely available. The description of the elementary methods in this article borrows from introductory notes by Stewart [31]. An excellent general reference on numerical inte ..."
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Cited by 2 (0 self)
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integration is [5]. More recent material can be found in [8] and [29]. Recent surveys of numerical integration with emphasis on statistical methods and applications are [10] and [9].
Numerical Integration of Stochastic Differential Equations
, 1995
"... Abstract. We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients. Following this concept, we discard the approximate trajectories which leave a sufficiently ..."
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Cited by 200 (12 self)
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Abstract. We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients. Following this concept, we discard the approximate trajectories which leave a
to numerical integration By
"... In this paper we propose special strategies to compute 1D integrals of functions having weakly or strong singularities at the endpoints of the interval of integration or complex poles close to the domain of integration. As application of the proposed strategies, we compute a four dimensional integra ..."
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integral arising from 3D Galerkin boundary element methods (BEM) applied to hypersingular boundary integral equations. In the computation of integrals and in the numerical solution of integral equations, one often has to deal with the numerical integration of functions with endpoint weak singularities
Numerical Integration
"... Introduction After transformation to a canonical element\Omega 0 , typical integrals in the element stiffness or mass matrices (cf. (5.5.8)) have the forms Q = ZZ \Omega 0 ff(; j)N s N T t det(J e )ddj; (6.1.1a) where ff(; j) depends on the coefficients of the partial differential equation an ..."
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Cited by 2 (0 self)
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Introduction After transformation to a canonical element\Omega 0 , typical integrals in the element stiffness or mass matrices (cf. (5.5.8)) have the forms Q = ZZ \Omega 0 ff(; j)N s N T t det(J e )ddj; (6.1.1a) where ff(; j) depends on the coefficients of the partial differential equation
and Numerical Integration
, 2002
"... I am submitting herewith a thesis written by Malachi Schram entitled ”Imple ..."
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I am submitting herewith a thesis written by Malachi Schram entitled ”Imple
Numerical Integration using Sparse Grids
 NUMER. ALGORITHMS
, 1998
"... We present and review algorithms for the numerical integration of multivariate functions defined over ddimensional cubes using several variants of the sparse grid method first introduced by Smolyak [51]. In this approach, multivariate quadrature formulas are constructed using combinations of tensor ..."
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Cited by 91 (16 self)
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We present and review algorithms for the numerical integration of multivariate functions defined over ddimensional cubes using several variants of the sparse grid method first introduced by Smolyak [51]. In this approach, multivariate quadrature formulas are constructed using combinations
Backward Error Analysis for Numerical Integrators
 SIAM J. Numer. Anal
, 1996
"... We consider backward error analysis of numerical approximations to ordinary differential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modified differential equation. A simple recursive definition of the modified equation is stated. This recursion is used ..."
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Cited by 110 (7 self)
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is used to give a new proof of the exponentially closeness of the numerical solutions and the solutions to an appropriate truncation of the modified equation. We also discuss qualitative properties of the modified equation and apply these results to the symplectic variable stepsize integration
Evaluation of numerical integration . . .
 RES. LETT. INF. MATH. SCI., 2005, VOL.7, PP171186
, 2005
"... This report evaluates two methodologies, finite differences and Fourier series, for numerically integrating a nonlinear neural model based on a partial integrodifferential equation. The stability and convergence criteria of four finite difference methods is investigated and their efficiency det ..."
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This report evaluates two methodologies, finite differences and Fourier series, for numerically integrating a nonlinear neural model based on a partial integrodifferential equation. The stability and convergence criteria of four finite difference methods is investigated and their efficiency
Results 1  10
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23,261