| 白象忠,田振国.离散正交法(DOM)离散点的正交分析与程序设计[J].计算力学学报,2006,23(6):678~683 |
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| 离散正交法(DOM)离散点的正交分析与程序设计 |
| Discrete orthogonal point analysis of discrete orthogonal method and program design |
| 修订日期：2004-08-21 |
| DOI：10.7511/jslx20066127 |
| 中文关键词: 离散正交法 边值问题 常微分方程组 数值方法 |
| 英文关键词:discrete orthogonal method,boundary value problem,ordinary differential equation,numerical method. |
| 基金项目:国家自然科学基金 |
| 白象忠 田振国 |
[1]燕山大学建筑工程与力学学院,秦皇岛066004 [2]中国科学院力学研究所国家非线性连续介质力学重点实验室(LNM)
,北京100080 |
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| 中文摘要: |
| 对能够求解一系列线性常微分方程组边值问题的数值计算方法——离散正交法（DOM）进行了离散点的正交分析，给出了计算机实现数值计算的程序设计原理与计算流程图，指出了该方法能够克服传统计算方法由于所求函数的快速增长所引起的边界效应和局部效应的缺点，给出了得到稳定计算过程的可能性。为了推广应用，文中介绍了离散正交法的基本原理、实现方法和求解过程．讨论了采用离散正交法来求解非线性问题的处理方法。并且以承受均布载荷的环形板为例，将采用离散正交法的计算结果与经典解作了对比。 |
| 英文摘要: |
| The orthogonal analysis of discrete points in a numerical method,discrete orthogonal method(DOM),which can be used to solve a series of boundary value problem of ordinary differential equations,is presented in this paper.The principle of program design and the flow chart of numerical computation are shown here.It indicates that the DOM conquers the disadvantage of traditional method,which often caused boundary and local effects due to the fast increasing of the value of a function.The possibility of stable calculation is illustrated.For generalizing application,the basic principle,fulfillment method and the performance progress of DOM are introduced.The treatment to solve non-linearly problem with DOM is discussed.An example of an annular plate applied equally distributed load is presented,and the calculation results obtained by DOM and traditional method respectively are compared. |
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