【摘要】 针对变分数阶扩散方程,提出新隐式差分法.首先,对二阶空间导数和Riemann-Liouville型变时间分数阶导数算子进行离散化处理,将变分数阶扩散方程转化为代数方程组求解;然后,借助Fourier级数技术给出了新隐式差分法的收敛性分析;最后,通过数值算例检验该方法,计算结果表明了新隐式差分法的可行性和有效性.更多还原

【Abstract】 A new implicit numerical difference method was proposed for the variable order fractional diffusion equation. Firstly,the second-order space derivative and the fractional-order time derivative could be discretized and used to transform the variable order fractional diffusion equation into a system of algebraic equations. Then,the convergence of the numerical method was discussed by Fourier analysis. Finally,some numerical examples were provided to test this method and the results demonstrated the feasibility and the efficiency of the proposed method.更多还原