The Siemens Community Catalyst program was co-created with our community to acknowledge technology leaders who consistently contribute to the Siemens Community. Nominations are accepted on a rolling basis.
時間積分公式として、中央差分法を用いた場合の安定限界に関して、もう少し詳しく見てみましょう。運動方程式:
に対して、中央差分:
を代入します。運動方程式は簡単のため減衰と外力を無視すると、
となるので、これに中央差分式:
、
を代入すると、
整理して、
より、以下の漸化式が得られます。
ここに、積分作用素行列は、
で、この固有値問題:
より根が次のように得られます。
安定条件:
より、を考慮すれば、結局、
と、Courantの安定条件が得られます。
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