| 求解偏微分方程的GD法原理及应用 |
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| 引用本文： | 罗光兵,彭建设.求解偏微分方程的GD法原理及应用[J].成都大学学报(自然科学版),2010,29(4):297-300. |
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| 作者姓名： | 罗光兵 彭建设 |
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| 作者单位： | 西南交通大学,牵引动力国家重点实验室,四川,成都,610031;成都大学,工业制造学院,四川,成都,610106 |
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| 基金项目： | 四川省科技厅应用基础资金资助项目 |
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| 摘 要： | GD法是从泰勒展开式出发,推出的一种求解偏微分方程的数值方法,该方法通过离散,将某节点的各阶导数表达为全域节点函数值的加权和,从而将偏微分方程转化为由待求节点函数值表述的代数方程组.系统地介绍了GD法的基本原理以及权系数的推导,并运用该方法求解了梁和薄板静力问题.计算结果表明,GD法具有数学原理严谨、精度高、收敛快、易于编程计算等特点,是求解偏微分方程的有力工具.
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| 关 键 词： | CD法 偏微分方程 矩形薄板 梁 挠度 |
Principle of GDM and Its Application for Solving Partial Differential Equations |
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| LUO Guangbing,PENG Jianshe.Principle of GDM and Its Application for Solving Partial Differential Equations[J].Journal of Chengdu University (Natural Science),2010,29(4):297-300. |
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| Authors: | LUO Guangbing PENG Jianshe |
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| Institution: | 1.Traction Power State Key Laboratory,Southwest Jiaotong University,Chengdu 610031,China;2.School of Industrial Manufacturing,Chengdu University,Chengdu 610106, China) |
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| Abstract: | GDM（General differential method） is a numerical method for solving partial differential equations based on Taylor series.Different order derivatives of a node are expressed as the weight sum of function values of nodes in the full boundary and partial differential equation can be changed into algebra equation set expressed by the function value of the nodes.The principle of GDM was described as well as the derivation of weight coefficients.The method was applied to solve the static problems of beam and rectangular plate.The results show that GDM has some merits such as precise,high accurate,good convergence,easy to program and it is a good tool for solving partial differential equations. |
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| Keywords: | general differential method partial differential equations rectangular plate beam deflection |
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