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Molecular Dynamics Simulations Through Symbolic Programming

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mirosław R. Dudek & Tadeusz Nadzieja, 2005. "Molecular Dynamics Simulations Through Symbolic Programming," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 413-425.
    • Handle: RePEc:wsi:ijmpcx:v:16:y:2005:i:03:n:s0129183105007212
    DOI: 10.1142/S0129183105007212
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