| 平面双调和问题的第一类边界积分方程的高精度求积方法与外推 |
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| 引用本文： | 吕涛,黄晋.平面双调和问题的第一类边界积分方程的高精度求积方法与外推[J].应用数学学报,2001,24(3):321-332. |
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| 作者姓名： | 吕涛 黄晋 |
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| 作者单位： | 四川大学数学学院,成都610064 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 借助位势理论，平面双调和方程的Dirichlet问题被转化为第一类边界积分方程组，本文使用新型的反常积分的求积公式构造出解造解此类边界积分方程的机械求积方法，证明了该方法具有O（h^3)阶精度和误差的h^3幂渐近展开，故借助Richardson外推还能提高精度阶。
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| 关 键 词： | 双调和方程 边界积分方程 求积方法 Dirichlet问题 Richardson外推 位势理论 精度阶 边界元法 |
QUADRATURE METHODS WITH HIGH ACCURACY AND THEIR EXTRAPOLATION FOR SOLVING BOUNDARY INTEGRAL EQUATIONS OF PLANE BIHARMONIC PROBLEMSGalois |
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| LU TAO HUANG JIN.QUADRATURE METHODS WITH HIGH ACCURACY AND THEIR EXTRAPOLATION FOR SOLVING BOUNDARY INTEGRAL EQUATIONS OF PLANE BIHARMONIC PROBLEMSGalois[J].Acta Mathematicae Applicatae Sinica,2001,24(3):321-332. |
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| Authors: | LU TAO HUANG JIN |
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| Abstract: | By means of potential theory, the biharmonic Dirichlet problem can be trans- fered to a boundary inteqral equation system of the first kind. This paper presents a quadra- ture method for solving boundary integral equation system of biharmonic Dirichlet problem, which possesses accuracy 0(h3). Moreover, the asymptotic expansion with h3 power of the error is shown, so we can improve the accuracy order of the approximations by Richardson extrapolation. |
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| Keywords: | biharmonic equation boundary integral equations quadrature method extrapolation |
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