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複素微分方程式

微分方程式
ナビエ–ストークス方程式。障害物の周囲の気流のシミュレーションに用いられる。
ナビエ–ストークス方程式。障害物の周囲の気流のシミュレーションに用いられる。
範囲
応用数学
社会科学
分類
タイプ
変数のタイプにより
特徴
過程との関係
解
一般的な話題
解法（英語版）
人物 (海外)
日本人

複素微分方程式（ふくそびぶんほうていしき、英: Complex differential equations）は、複素関数を厳密解としてもつ微分方程式の総称であり、その解析には解析接続やモノドロミー行列をはじめとした複素解析の道具が用いられる[1][2][3][4]。

主な複素微分方程式

主な複素常微分方程式

→「常微分方程式」も参照

主な複素偏微分方程式

→「偏微分方程式」も参照

研究者

日本

海外

関連項目

出典

[脚注の使い方]
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参考文献

  • Einar Hille (1976). Ordinary Differential Equations in the Complex Domain. Wiley. ISBN 978-0-471-39964-3., reprinted by Dover, 1997.
  • E. Ince (1926). Ordinary Differential Equations. Dover., reprinted by Dover, 2003.
  • Gromak, Laine, Shimomura (2002). Painlevé Differential Equations in the Complex Plane. de Gruyter. ISBN 978-3-11-017379-6.
  • Ilpo Laine (1992). Nevanlinna Theory and Complex Differential Equations. de Gruyter. ISBN 978-3-11-013422-3.
  • Eremenko, A. (1982). "Meromorphic solutions of algebraic differential equations". Russian Mathematical Surveys. 37 (4): 61–94. CiteSeerX 10.1.1.139.8499. doi:10.1070/RM1982v037n04ABEH003967.
  • So-Chin Chen; Mei-Chi Shaw (2002). Partial Differential Equations in Several Complex Variables. American Mathematical Society. ISBN 978-0-8218-2961-5.
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