複素微分方程式
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微分方程式 |
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分類 |
解 |
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
[編集]主な複素常微分方程式
[編集]「常微分方程式」も参照
主な複素偏微分方程式
[編集]「偏微分方程式」も参照
研究者
[編集]日本
[編集]海外
[編集]関連項目
[編集]- フックス型微分方程式[3]
- コーシー=コワレフスカヤの定理
- クニーズニク・ザモロドチコフ方程式[83]
- en:Riemann–Hilbert problem[1][3][77][84]
- en:Riemann–Hilbert correspondence
出典
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参考文献
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- Einar Hille (1976). Ordinary Differential Equations in the Complex Domain. Wiley. ISBN 978-0-471-39964-3., reprinted by Dover, 1997.
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- So-Chin Chen; Mei-Chi Shaw (2002). Partial Differential Equations in Several Complex Variables. American Mathematical Society. ISBN 978-0-8218-2961-5.