| 求解对流扩散方程的4阶紧致差分格式 |
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| 引用本文： | 李冉冉,王红玉,开依沙尔·热合曼. 求解对流扩散方程的4阶紧致差分格式[J]. 江西师范大学学报(自然科学版), 2022, 0(5): 517-522. DOI: 10.16357/j.cnki.issn1000-5862.2022.05.12 |
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| 作者姓名： | 李冉冉 王红玉 开依沙尔·热合曼 |
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| 作者单位： | (新疆大学数学与系统科学学院,新疆 乌鲁木齐 830046) |
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| 摘 要： | 该文提出了在周期和Dirichlet边界条件下的1维对流扩散方程的紧致差分格式.在这2种边界条件下对空间变量使用4阶紧致差分格式,对时间变量利用3次Hermite插值公式构造空间和时间同时具有4阶精度的数值格式,并证明了格式的绝对稳定性,最后通过对2种边界条件下的算例进行数值实验和比较,验证了格式的精确性和可靠性.
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| 关 键 词： | 对流扩散方程 紧致差分格式 Hermite插值 Dirichlet边界条件 |
The Fourth-Order Compact Finite Difference Scheme for the Convection Diffusion Equation |
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| LI Ranran,WANG Hongyu,KAYSAR Rahman. The Fourth-Order Compact Finite Difference Scheme for the Convection Diffusion Equation[J]. Journal of Jiangxi Normal University (Natural Sciences Edition), 2022, 0(5): 517-522. DOI: 10.16357/j.cnki.issn1000-5862.2022.05.12 |
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| Authors: | LI Ranran WANG Hongyu KAYSAR Rahman |
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| Affiliation: | (College of Mathematics and System Science,Xinjiang University,Urumqi Xinjiang 830046,China) |
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| Abstract: | In this paper,a compact difference scheme for the one-dimensional convection diffusion equation under periodic and Dirichlet boundary conditions is proposed.The fourth-order compact difference scheme is used for the spatial variables under these two boundary conditions,and the numerical scheme with both spatial and temporal fourth-order accuracy is constructed using the cubic Hermite interpolation formula for the temporal variables.Finally,the accuracy and reliability of the scheme is verified by numerical experiments and comparisons of numerical examples under two boundary conditions. |
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| Keywords: | convection diffusion equation high-order compact finite difference Hermite formula Dirichlet boundary conditions |
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