| 一类时间分数阶线性扩散方程的数值方法 |
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| 引用本文： | 张艳敏.一类时间分数阶线性扩散方程的数值方法[J].曲阜师范大学学报,2014(3):17-20. |
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| 作者姓名： | 张艳敏 |
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| 作者单位： | 青岛理工大学琴岛学院; |
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| 基金项目： | 国家自然科学基金(11271101) |
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| 摘 要： | 利用非标准有限差分法给出了求解一类时间分数阶线性扩散方程的一种数值解法.对时间分数阶导数和整数阶空间导数离散后的差分近似过程中,对分母构造了一个关于时间步长和空间步长的函数来近似,证明了该差分格式是收敛和稳定的,通过数值算例验证该方法是有效的.
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| 关 键 词： | 线性 时间分数阶扩散方程 非标准有限差分格式 无条件收敛 无条件稳定 |
A Numerical Method for Solving One Time Fractional Linear Diffusion Equation |
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| Institution: | CHI Guang-sheng, ZHANG Fang, SUN Chun-long, DU Dian-hu (1 Department of Basic Courses,Shandong Kaiwen College of Science ＆ Technology,250200,Jinan;2Institute of Applied Mathematics,School of Science,Shandong University of Technology,255000,Zibo,Shandong,PRC) |
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| Abstract: | Nonstandard finite difference method is presented to solve one time fractional linear diffusion equation.The time fractional derivative and space derivative are discrete,but the denominator functions of the difference equations are space step and time step functions.The difference scheme is unconditional stable and convergence.Numerical example shows that the numerical method is practical. |
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| Keywords: | linear time fractional diffusion equation nonstandard finite difference method unconditional convergence unconditional stable |
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