| 边值问题中与分离变量法等价的级数解法 |
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| 引用本文： | 严湘赣,武际可.边值问题中与分离变量法等价的级数解法[J].固体力学学报,1998,19(2):127-132. |
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| 作者姓名： | 严湘赣 武际可 |
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| 作者单位： | 北京大学力学与工程科学系 |
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| 基金项目： | 国家自然科学基金,国家教委博士点基金 |
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| 摘 要： | 用带奇性分离的Ｆｏｕｒｉｅｒ级数解平面边值问题，改进了不能满足全部边界条件的一般级数解法，得到收敛较好的解析算法。文中证明了级数解法与分离变量法的等价性，由此将分离变量解所得的非线性特征方程转化为多项式方程，为近似算法与渐近分析提供了依据。
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| 关 键 词： | 级数解 分离变量法 边值问题 特征方程 |
A SPECIAL METHOD OF FOURIER SERIES WHICH IS EQUAL TO THE METHOD OF SEPARATION OF VARIABLES ON BOUNDARY VALUE PROBLEM |
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| Yan Xianggan,Wu Jike.A SPECIAL METHOD OF FOURIER SERIES WHICH IS EQUAL TO THE METHOD OF SEPARATION OF VARIABLES ON BOUNDARY VALUE PROBLEM[J].Acta Mechnica Solida Sinica,1998,19(2):127-132. |
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| Authors: | Yan Xianggan Wu Jike |
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| Abstract: | By separation of singularity, a special Fourier series solution of the boundary value problem for planes is obtained, which can satisfy all boundary conditions and converge rapidly. It is proved that the solution is equal to the result of separation of variables. As a result, the non linear characteristic equations resulted from the method of separation of variables are transformed into polynomial equations which can provide a foundation for approximate computation and asymptotic analysis. |
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| Keywords: | separation of singularity series resolusion method of separation of variables boundary value problem characteristic equation |
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