Application of Computer Algebra for the Method of Multiple Scales.

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  • 多重尺度法に対する数式処理システムの応用
  • タジュウ シャクドホウ ニ タイスル スウシキ ショリ システム ノ オウヨウ

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The massive algebraic calculation is usually required to carry out the higher order analysis by perturbation method. In this paper, the method of multiple scales is automated on Computer algebra (REDUCE 3.3) by introducing a new operator, so that the higher order analysis, which is unthinkable by hand calculation, can be accomplished. By applying this algorithm, the 6th order analysis of the typical nonlinear dynamical system, as well as expressed by a nonlinear differential equation with a periodic coefficient and a nonhomogeneous term, is quickly and accurately performed. Furthermore, by comparing the above approximate solution with the numerical one, it is shown that the 6th order approximation is effective.

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