M.M. Chawla. On the order and attainable intervals of periodicity of explicit Nystroem methods for y 00 = f(t; y). SIAM J. Numer. Anal., 22:127--131, 1985. Home/Search Document Not in Database Summary Related Articles Check |
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Smoothed Molecular Dynamics For Thermally Embedded Systems - Schütte (1995) (Correct)
....we have to resolve this timescale, i.e. we have to choose stepsizes 1 fs in the time discretization. And even if accuracy is less important we have to use 1 fs in order to ensure numerical stability for the iteration of the discretization (at least for all conventional explicit discretizations [1]; for most implicit methods similar stepsize bounds result from the requirement of unique convergence of the iterative solution of the nonlinear equations in each step) The typical time length of an MD simulation is t max AE 1 ps. Therefore we have to make a large number t max = of time steps, ....
M.M. Chawla. On the order and attainable intervals of periodicity of explicit Nystroem methods for y 00 = f(t; y). SIAM J. Numer. Anal., 22:127--131, 1985.
Integration Methods for Molecular Dynamics - Leimkuhler, Reich, Skeel (1994) (3 citations) (Correct)
....slight shrinking. In a sequence of Verlet steps the intermediate stretchings and shrinkings all cancel. This does not happen though if the method or the timestep is varied. The restriction Deltat 2, which is necessary for stability, is the weakest restriction of any conventional explicit method [11]. An important property of the Verlet method is that it is symplectic. We will now describe this property. 3 Symplectic discretizations In two dimensions, a mapping is symplectic if it is area preserving: any bounded region is mapped to another region of equal area. In higher dimensions, ....
Chawla, M.M., On the order and attainable intervals of periodicity of explicit Nystrom methods for y" = f(t; y), SIAM J. Numer. Anal. 22, 127--131, 1985.
Integration Methods for Molecular Dynamics - Leimkuhler, Reich, Skeel (1996) (3 citations) (Correct)
....shrinking. In a sequence of Verlet steps the intermediate stretchings and shrinkings all cancel. This does not happen though if the method or the timestep is varied. The restriction Deltat 2, which is necessary for stability, is the weakest restriction of any conventional explicit method [11]. An important property of the Verlet method is that it is symplectic. We will now describe this property. IMA, LeiReiSke, May 26, 1995 7 3 Symplectic discretizations In two dimensions, a mapping is symplectic if it is area preserving: any bounded region is mapped to another region of equal ....
Chawla, M.M., On the order and attainable intervals of periodicity of explicit Nystrom methods for y" = f(t; y), SIAM J. Numer. Anal. 22, 127--131, 1985.
Eighth-order Explicit Symplectic Runge-Kutta-Nyström Integrators - Okunbor, Lu (1994) (1 citation) (Correct)
.... h 2 b T (I h 2 A) Gamma1 c) Gamma hB T (I h 2 A) Gamma1 e 1 Gamma h 2 B T (I h 2 A) Gamma1 c ; provided (I h 2 A) Gamma1 exists. An RKN method is said to be P stable if and only if ae( Omega Gamma = 1: The interval of periodicity[4] is defined as [0; h 0 ] where h 0 is the greatest value such that ae( Omega Gamma h) 1; for 0 h h 0 : Let tr( h) and det( h) be the trace and determinant, respectively, of Omega Gamma h) The eigenvalues of Omega Gamma h) are tr( h) 2 Sigma i s det( ....
....Suris[11] a consistent symplectic RKN method is P stable for sufficiently small time step h. Treating the requirement Gamma2 tr( h) 2 as minimax problem and using the fact that tr( h) behaves at best like T s (1 Gamma hff 1 2s 2 ) where T s (x) is a Tchebyshev polynomial, Chawla[4] was able to show that the optimal scaled interval of P stability is [ Gamma2; 2] for a consistent s stage RKN method. In fact, he had shown that for methods of orders higher than 2, the length of the scaled interval of P stability is always less than 2. The expression for tr( h) grows ....
M. M. Chawla. On the order and attainable intervals of periodicity of explicit Nystrom methods for y 00 = f(t; y). Physica D, 43:105--117, 1990.
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