| 刘庆潭.扩散方程单内点精细积分法与差分法比较研究[J].计算力学学报,1996,13(3): |
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| 扩散方程单内点精细积分法与差分法比较研究 |
| Comparative study of the one point high precise integration method and the finite difference methods for diffusion equations |
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| DOI：10.7511/jslx19963053 |
| 中文关键词: 稳定性／传递矩阵 变截面压杆 |
| 英文关键词:initial problem of diffusion equations,numerical solution of partial differential equations,high precise integration method |
| 基金项目: |
| 刘庆潭 |
| 长沙铁道学院 |
| 摘要点击次数: 1149 |
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| 中文摘要: |
| 一维扩散方程初值问题可以用全域或子域精细积分求解。子域积分可以采用不同数量的内点，单内点是其最简单的情况。当单内点精细积分中的传递函数即指数函数用其泰勒展开式的一阶近似来替代时，精细积分转化为差分方程。本文研究了这一对应关系。各种常见差分格式均找到了对应的单点精细积分格式，并在单点精细积分一般公式中得到了统一表达形式 |
| 英文摘要: |
| The initial problem of one dimensional diffusion equations can be solved by using global or sub domain high precise integration method.One point high precise integration method is the simplest case of this method.When the exponential function in this method is replaced by different expressions of its approximation,this method is transferred to different finite difference methods.Comparative study of these two methods is made in this paper.Different kinds of finite difference method can be expressed in terms of the corresponding approximations of one point high precise integration method. |
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