二维空间分数阶变系数扩散方程的数值解法 |
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引用本文: | 池光胜,张芳,孙春龙,杜殿虎. 二维空间分数阶变系数扩散方程的数值解法[J]. 曲阜师范大学学报, 2014, 0(3): 13-16 |
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作者姓名: | 池光胜 张芳 孙春龙 杜殿虎 |
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作者单位: | 山东凯文科技职业学院基础教学部;山东理工大学理学院应用数学研究所; |
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基金项目: | 山东凯文科技职业学院校自然科学基金项目(KW2012-09) |
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摘 要: | 研究二维有限域上的扩散系数与空间变量相关的空间分数阶扩散方程,通过移位的Grunwald公式对空间分数阶导数进行离散,得到交替差分格式,证明了格式的稳定性,最后给出了数值算例.
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关 键 词: | 二维分数阶扩散方程 交替差分格式 稳定性 数值求解 |
Numerical Methods for the Two-dimensional Space Fractional Diffusion Equations with Variable Coefficients |
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Affiliation: | CHI Guang-sheng, ZHANG Fang, SUN Chun-long, DU Dian-hu(1 Department of Basic Courses,Shandong Kaiwen College of Science & Technology,250200,Jinan;2 Institute of Applied Mathematics,School of Science,Shandong University of Technology,255000,Zibo,Shandong,PRC) |
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Abstract: | A numerical method for two-dimensional fractional diffusion equations with variable coefficient which the fractional derivative can be approximated by the shifted Grunwald-formula on a finite domain is discussed.The ADI alternating directions are obtained by implicit method,the stability is proved by Fourier transformation.Finally,a numerical example is given. |
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Keywords: | two-dimensional fractional diffusion equation ADI implicit method stability numerical example |
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