| 二阶椭圆型方程的广义解析解 |
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| 引用本文： | 欧阳华江,钟万勰,杨琦,邓子辰. 二阶椭圆型方程的广义解析解[J]. 大连理工大学学报, 1993, 0(3) |
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| 作者姓名： | 欧阳华江 钟万勰 杨琦 邓子辰 |
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| 作者单位： | 大连理工大学工程力学研究所(欧阳华江，钟万勰，杨琦)，大连理工大学工程力学研究所(邓子辰) |
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| 摘 要： | 给出一种刚提出的基于Ｈａｍｉｌｔｏｎ体系的解析法的各个步骤，并用这种方法首次求出了矩形域上二阶非齐次椭圆型方程的广义解析解．这种方法具有一定的普遍意义，还可求解某些尚未获解的偏微分方程．通过算例验证了解答的正确性．
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| 关 键 词： | 椭圆型方程 解析解 分离变量法 Hamilton方程 辛 正交 |
Analytic solution of non-homogeneous two-order elliptic equation |
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| Ouyang Huajiang,Zhong Wanxie,Yang Qi,Deng Zichen. Analytic solution of non-homogeneous two-order elliptic equation[J]. Journal of Dalian University of Technology, 1993, 0(3) |
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| Authors: | Ouyang Huajiang Zhong Wanxie Yang Qi Deng Zichen |
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| Abstract: | All the steps of a new, Hamiltonian-system - based analytic met hed put forward by the second author,are presented and used to obtain for the first time the analytic solution of general non- homogeneous two-order elliptic equation on rectangular domain. The method is a generalization of classical method of separation of variables based on the adjoint symplectic orthogonality for solving some non-self-adjoint partial differential operators. As a verification,the analytic solution is found very close to the numerical results by Ritz method and finite element methed. The idea can also be used to solve some PDEs of higher dimensions. |
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| Keywords: | elliptic equations analytic solutions separation of variables Hamilton's equations partial differential equations symplectic orthogonality |
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