MOLECULAR DYNAMICS SIMULATIONS THROUGH SYMBOLIC PROGRAMMING

Mirosław R. Dudek () and Tadeusz Nadzieja ()
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Mirosław R. Dudek: Institute of Physics, University of Zielona Góra, 65-069 Zielona Góra, Poland
Tadeusz Nadzieja: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, 65-069 Zielona Góra, Poland

International Journal of Modern Physics C (IJMPC), 2005, vol. 16, issue 03, 413-425

Abstract: We present an algorithm for the Cauchy problem for the ordinary differential equations which is based on symbolic programming. It is complementary to numerical methods, which use the finite differences. The algorithm consists of two steps. First, it yields a set of polynomials of a given degreenin some formal parameter λ. They represent an analytic form of the truncated solution of the system of differential equations under consideration and the larger value ofnthe larger interval in which this approximation satisfies the chosen accuracy criterion. We putλ = 1afterall. The second step is purely numerical. Namely, the numerical values of the polynomials in the interval, in which the difference between them and the polynomials of the smaller degreen - j(for certainj) does not exceed a given accuracy ε, become the numerical solution. In the point, where this accuracy criterion fails the new initial values are defined, just at this "disagreement point", and the whole procedure is repeated.

Keywords: Molecular dynamics simulations; differential equation; initial-value problem; symbolic computation; 02.70.Ns; 02.70.Wz (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1142/S0129183105007212

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