时间分数阶扩散方程的一个新的高阶数值格式
A NEW HIGH ORDER NUMERICAL SCHEME TO THE TIME FRACTIONAL DIFFUSION EQUATIONS
查看参考文献15篇
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文摘
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研究时间分数阶扩散方程,利用时间方向的有限差分格式和空间方向的Legendre collocation 谱方法构造了一个高阶稳定格式.一系列的数值试验表明该格式是稳定的,其收敛阶为O(△t~(3-α)+ N~(-m)),这里α, △t,N和m分别为时间分数阶导数的阶数、时间步长、空间多项式逼近阶数和精确解的正则度. |
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其他语种文摘
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We investigate the time fractional anomalous diffusion equation on a bounded domain. We propose an efficient method for its numerical solution. This method is based on a finite difference in time and spectral method in space. The numerical examples show the convergence rate is O(△t~(3-α) + N~(-m)), where a, At, N and m are respectively the order of time fractional derivatives, time step size, the polynomial degree and the regularity of the exact solution. |
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来源
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数值计算与计算机应用
,2014,35(4):277-288 【扩展库】
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关键词
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时间分数阶扩散方程
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高阶数值方法
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差分法
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谱方法
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地址
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贵州民族大学理学院, 贵阳, 550025
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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1000-3266 |
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学科
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自动化技术、计算机技术 |
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基金
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国家自然科学基金
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贵州省自然科学基金
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贵州省教育厅
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文献收藏号
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CSCD:5310348
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参考文献 共
15
共1页
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