| 解抛物型方程的一族六点隐式差分格式 |
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| 引用本文： | 詹涌强. 解抛物型方程的一族六点隐式差分格式[J]. 安徽大学学报(自然科学版), 2012, 0(4): 26-29 |
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| 作者姓名： | 詹涌强 |
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| 作者单位： | 华南理工大学广州学院基础部数学教研室 |
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| 基金项目： | 国家自然科学基金资助项目(61070165);广东省科技计划基金资助项目(2009B01080030) |
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| 摘 要： | 提出了求解一维抛物型方程的一族两层六点隐式格式.格式的截断误差为O(τ2+h4).利用Fourier方法证明了差分格式当1/2≤θ≤1时,格式绝对稳定;当0≤θ1/2时,只有r≤1/6(1-2θ),格式才是稳定的.数值试验表明,该族格式是有效的,且理论分析与实际计算相吻合.
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| 关 键 词： | 一维抛物型方程 隐式差分格式 截断误差 |
A class of implicit difference schemes of six points for solving the parabolic equations |
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| ZHAN Yong-qiang. A class of implicit difference schemes of six points for solving the parabolic equations[J]. Journal of Anhui University(Natural Sciences), 2012, 0(4): 26-29 |
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| Authors: | ZHAN Yong-qiang |
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| Affiliation: | ZHAN Yong-qiang(Department of Mathematics Education,Guangzhou College of South China University of Technology,Guangzhou 510800,China) |
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| Abstract: | Proposed in the paper was a class of two-level implicit difference schemes for solving one-dimension parabolic equation.The truncation error of the scheme was O(τ2+h4).By Fourier method,the difference scheme was proved to be unconditionally stable if1/2≤θ≤1,and the stability condition was0
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| Keywords: | one-dimension parabolic equation implicit difference schemes truncation error |
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