| 求解间断边值问题的重心插值单元配点法 |
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| 引用本文： | 王兆清,唐炳涛,李树忱,李淑萍. 求解间断边值问题的重心插值单元配点法[J]. 山东建筑工程学院学报, 2009, 0(2) |
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| 作者姓名： | 王兆清 唐炳涛 李树忱 李淑萍 |
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| 作者单位： | 山东建筑大学工程结构现代分析与设计研究所;山东大学土建与水利学院;山东警察学院治安系; |
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| 基金项目： | 国家自然科学基金资助项目(50727904);;山东建筑大学博士科研启动基金、科研基金资助项目(XN050103) |
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| 摘 要： | 按照间断边值问题的连续区间划分计算单元,在每一个单元上采用重心Lagrange插值近似未知函数,得到每一个单元上的微分矩阵。利用微分矩阵离散微分算子,得到每一个单元上微分方程的离散代数方程组,组装得到边值问题求解的整体代数方程组。将边界条件和单元间的连续性条件,利用微分矩阵离散为代数方程,采用置换法施加边界条件和单元间的连续性条件,得到修正的代数方程组,求解代数方程组得到节点处的函数值。二阶和三阶间断边值问题的数值算例验证了本文方法的有效性和计算精度。
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| 关 键 词： | 间断边值问题 重心Lagrange插值 重心插值单元法 单元配点法 |
Element-based collocation method of barycentric interpolation for solving discontinuous boundary value problems |
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| WANG Zhao-qing,TANG Bing-tao,LI Shu-chen,et al.. Element-based collocation method of barycentric interpolation for solving discontinuous boundary value problems[J]. Journal of Shandong Institute of Architecture and Engineering, 2009, 0(2) |
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| Authors: | WANG Zhao-qing TANG Bing-tao LI Shu-chen et al. |
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| Affiliation: | 1.Institute of Modern Analysis & Design for Engineering Structures;Shandong Jianzhu University;Jinan 250101;China;2.School of Civil Engineering;Shandong University;Jinan 250061;China |
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| Abstract: | Differential matrices are obtained on the element in accordance with continuous intervals of discontinuous boundary value problem to divide the computing elements and approximating unknown function on the element in term of barycentric Lagrange interpolation.The discrete algebraic equation system on the element is constructed by using differential matrices.The global algebraic equations system of discontinuous boundary value problem is obtained by assembled algebraic equation systems on elements.Discreting ... |
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| Keywords: | discontinuous boundary value problems barycentric Lagrange interpolation barycentric interpolation element method element-based collocation method |
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