| 变时间分数阶扩散方程的非一致时间网格有限差分方法 |
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| 引用本文： | 姜英军,蒙玲玲.变时间分数阶扩散方程的非一致时间网格有限差分方法[J].数学理论与应用,2014(4):6-11. |
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| 作者姓名： | 姜英军 蒙玲玲 |
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| 作者单位： | 长沙理工大学数学与计算科学学院,长沙410004 |
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| 摘 要： | 本文在非一致时间网格上,使用有限差分方法求解变时间分数阶扩散方程?α(x,t)u(x,t)/tα(x,t)-2u(x,t)/x2=f(x,t),0α(x,t)q≤1,证明了该方法在最大范数下的稳定性与收敛性,收敛阶为C(Δt2-q+h2).数值实例验证了理论分析的结果.
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| 关 键 词： | 时间分数阶扩散方程 变分数阶 非一致网格 |
A Finite Difference Method Based on Non- uniform Time Grids for a Variable- order Time Fractional Diffusion Equation |
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| Jiang Yingjun School of Mathematics and Computer Science,Meng Lingling.A Finite Difference Method Based on Non- uniform Time Grids for a Variable- order Time Fractional Diffusion Equation[J].Mathematical Theory and Applications,2014(4):6-11. |
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| Authors: | Jiang Yingjun School of Mathematics and Computer Science Meng Lingling |
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| Institution: | Changsha University of Science and Technology, Changsha 410004, China) |
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| Abstract: | A finite difference method based on non - uniform time grids is presented to solve the variable - order time fractional diffusion equation δα（x,t）u（x,t）/δtα（x,t）-δ^2u（x,t）/δx^2=f（x,t）,0〈α（x,t）〈q≤1 The stability and convergence of the method are proved under the maximum norm, and the convergence order is C（△t^2-q＋h^2）.Numerical tests are conducted to support the results of the theoretical analysis. |
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| Keywords: | Time fractional diffusion equation Variable -order Non -uniform grids |
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