| 一维变系数对流扩散方程的一个紧致差分格式 |
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| 引用本文： | 王倩倩,李鑫,孙启航.一维变系数对流扩散方程的一个紧致差分格式[J].徐州师范大学学报(自然科学版),2013(3):21-24. |
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| 作者姓名： | 王倩倩 李鑫 孙启航 |
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| 作者单位： | [1]南京航空航天大学理学院,江苏南京210016 [2]安徽科技学院理学院,安徽凤阳233100 [3]鲁东大学信息与电气工程学院,山东烟台264005 |
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| 摘 要： | 对一维变系数的对流扩散方程提出了一个紧致差分格式,从而将格式的收敛阶提高为O(τ2+h4),通过Fourier级数的方法和Lax等价性定理证明了差分格式的稳定性和收敛性,数值实验结果很好地验证了理论的正确性.
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| 关 键 词： | 变系数 对流扩散 紧致差分格式 收敛性 稳定性 |
A compact finite difference scheme for 1D convection-diffusion equations with variable coefficients |
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| Wang Qianqian,Li Xin,Sun Qihang.A compact finite difference scheme for 1D convection-diffusion equations with variable coefficients[J].Journal of Xuzhou Normal University(Natural Science Edition),2013(3):21-24. |
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| Authors: | Wang Qianqian Li Xin Sun Qihang |
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| Institution: | 1. College of Seience,Nanjing University of Aeronautics ＆ Astronautics,Nanjing 210016,Jiangsu,China; 2. School of Science, Anhui Science ＆ Technology University, Fengyang 233100, Anhui, China; 3. College of Information ＆ Electrical Engineering, Ludong University, Yantai 264005, Shandong, China) |
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| Abstract: | In this paper, a compact finite difference scheme is presented for 1D convection-diffusion equations with variable coefficients. The convergence order is O（v2 q- h4 ）. The stability and convergence are proved by Fourier method and Lax equivalence theorem. The numerical results have been carried out to confirm the correctness of the theory. |
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| Keywords: | variable coefficient convection-diffusion compact finite difference scheme convergence stability |
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