| 求解热传导方程的一族三层隐式差分格式 |
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| 引用本文： | 詹涌强. 求解热传导方程的一族三层隐式差分格式[J]. 湖北大学学报(自然科学版), 2012, 34(2): 235-238 |
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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,广东广州,510800 |
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| 基金项目： | 国家自然科学基金，广东省科技计划项目 |
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| 摘 要： | 提出求解热传导方程的一族高精度三层九点隐式格式,格式的截断误差为O(τ2+h4).利用Fourier方法证明差分格式是绝对稳定的.并通过数值试验,比较差分格式的解和精确解,说明差分格式的有效性.
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| 关 键 词： | 热传导方程 高精度 隐式差分格式 绝对稳定 |
A class of three-level implicit difference scheme for solving heat-conduction equation |
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| ZHAN Yongqiang. A class of three-level implicit difference scheme for solving heat-conduction equation[J]. Journal of Hubei University(Natural Science Edition), 2012, 34(2): 235-238 |
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| Authors: | ZHAN Yongqiang |
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| Affiliation: | ZHAN Yongqiang(Department of Mathematics Education,Guangzhou College of South China University of Technology, Guangzhou 510800,China) |
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| Abstract: | It proposed a class of three-level implicit difference scheme with high accuracy for solving heat-conduction equation,and the truncation error of the scheme was Oτ2+h4.The difference scheme was proved to be unconditionally stable by Fourier method.The numerical experiment showed the numerical solutions of difference scheme and the precise solutions were matched and the difference scheme was effective. |
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| Keywords: | heat-conduction equation high-order accuracy implicit difference scheme absolutely stability |
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