| 分数阶Burgers方程的有限元计算(英文) |
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| 引用本文： | 吴小伴,曾凡海.分数阶Burgers方程的有限元计算(英文)[J].应用数学与计算数学学报,2012,26(2):160-175. |
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| 作者姓名： | 吴小伴 曾凡海 |
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| 作者单位： | 上海大学理学院,上海,200444 |
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| 基金项目： | supported by the Key Program of Shanghai Municipal Education Commission(12ZZ084);the Key Disciplines of Shanghai Municipality(S30104) |
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| 摘 要： | 建立了一维和二维分数阶Burgers方程的有限元格式.时间分数阶导数使用L1方法离散,空间方向使用有限元方法离散.通过选择合适的基函数,将离散后的方程转化成一个非线性代数方程组,并应用牛顿迭代方法求解.数值实验显示出了方法的有效性.
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| 关 键 词： | 分数阶Burgers方程 Caputo导数 Riemman-Liouville导数 有限元方法 牛顿法 |
Finite element computation of fractional Burgers equation |
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| WU Xiao-ban,ZENG Fan-hai.Finite element computation of fractional Burgers equation[J].Communication on Applied Mathematics and Computation,2012,26(2):160-175. |
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| Authors: | WU Xiao-ban ZENG Fan-hai |
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| Institution: | (College of Sciences,Shanghai University,Shanghai 200444,China) |
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| Abstract: | The finite element formulations are developed to solve the fractional Burgers equations in one and two dimension.The time fractional derivative is discretized by the L1 scheme,and the space direction is approximated by the finite element method.The established methods lead to the nonlinear algebraic systems, which are solved by Newton’s method at each time step.Numerical examples are presented to show the good performance of the derived methods. |
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| Keywords: | fractional Burgers equation Caputo derivative Riemman-Liouvillederivative finite element method Newton's method |
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