A Simple Algorithm to Solve Non-linear Equations with Multiple Roots of Two Variables Appearing in Autocatalytic Reaction in Open Systems.

  • SAGAN Amih
    National Institute of Materials and Chemical Research 1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan
  • NAGASHIMA Umpei
    National Institute of Materials and Chemical Research 1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan
  • MORI Yoshihito
    Department of Chemistry, Faculty of Science, Ochanomizu University 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan

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Other Title
  • 自己触媒反応に現れる多根を持つ2変数の非線形方程式の簡便な数値解法
  • ジコ ショクバイ ハンノウ ニ アラワレル タコン オ モツ 2 ヘンスウ ノ ヒセンケイ ホウテイシキ ノ カンベン ナ スウチカイホウ

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Abstract

We propose a simple computational algorithm to solve non-linear equations with multiple roots of two variables: F(x,y)=0. The algorithm is effective only where the relationship between two variables x and y is monotonous and continuous (for example, see Fig.s 1 and 3). The algorithm also gives a guideline of automatic adjustment of the notch width in the Euler method. The efficiency of the algorithm was demonstrated by analyzing two typical examples and an autocatalytic reaction in open systems.

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