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On the internal stepsize of an extrapolation algorithm for IVP in ODE

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Abstract

We propose an extrapolation algorithm for initial value problems in ordinary differential equations. In the algorithm, an appropriately chosen stepsizeH is divided into smaller stepsizes by a sequence and a new stopping rule is proposed. The sequences applied to the algorithm are Romberg {2,4,8,16,32,...}, Bulirsch {2,4,6,8,16...} and Harmonic {2,4,6,8,10,12,...} types. The proposed algorithm is compared numerically with the algorithm introduced by Stoer. In view of the accuracy of numerical solutions, the relatively small number of calculations, the stability and reliability of the algorithm, we found that the algorithm with the Romberg sequence is the best.

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Authors and Affiliations

  1. Department of Electronics, The Institute of Vocational Training, 1960 Aihara, 229, Sagamihara, Kanagawa, Japan

    Makoto Murofushi

  2. Department of Mathematics, College of Science and Technology, Nihon University, 1-8 Surugadai Kanda, 101, Chiyodaku, Tokyo, Japan

    Hideko Nagasaka

Authors
  1. Makoto Murofushi
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  2. Hideko Nagasaka
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Murofushi, M., Nagasaka, H. On the internal stepsize of an extrapolation algorithm for IVP in ODE. Numer Algor 3, 321–334 (1992). https://doi.org/10.1007/BF02141940

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