论文标题
通用分数扩散方程的高阶数值方案
High Order Numerical Scheme for Generalized Fractional Diffusion Equations
论文作者
论文摘要
在本文中，提出了针对广义分数扩散方程（GFDES）提出的高阶差异方案。根据定义中使用比例和权重函数的广义分数衍生物（GFD），考虑了分数扩散方程。在特定情况下，GFD减少了Riemann-Liouville，Caputo衍生物和其他分数衍生物。由于量表的重要性以及重量功能在描述现实生活中物理系统的行为方面，我们通过考虑各种规模和权重功能来介绍GFDES的解决方案。还讨论了有限差异方案（FD）的收敛性和稳定性分析，以验证所提出的方法。我们考虑了FD的数值模拟的测试示例，以证明提出的数值方法是合理的。
In this paper, a higher order finite difference scheme is proposed for Generalized Fractional Diffusion Equations (GFDEs). The fractional diffusion equation is considered in terms of the generalized fractional derivatives (GFDs) which uses the scale and weight functions in the definition. The GFD reduces to the Riemann-Liouville, Caputo derivatives and other fractional derivatives in a particular case. Due to importance of the scale and the weight functions in describing behaviour of real-life physical systems, we present the solutions of the GFDEs by considering various scale and weight functions. The convergence and stability analysis are also discussed for finite difference scheme (FDS) to validate the proposed method. We consider test examples for numerical simulation of FDS to justify the proposed numerical method.
