论文标题
对于一般边界条件的高维空间 - 分数反应扩散方程的快速准确的高级方法
Fast and accurate high-order method for high dimensional space-fractional reaction-diffusion equation with general boundary conditions
论文作者
论文摘要
为了实现有效，准确的长时间整合，我们提出了一种快速，准确稳定的高阶数值方法，用于求解空间空间反应 - 扩散方程。所提出的方法在本质上是显式的，并利用了具有基于FFT的实现的空间中的四阶有限差异方案和矩阵转移技术（MTT）。时间积分是通过准确的四阶修改指数时间差异runge-kutta方案完成的。线性稳定性分析和各种数值实验，包括二维（2D）Fitzhugh-Nagumo，Gierer-Meinhardt，Gray-Scott和三维（3D）Schnakenberg模型，以证明提议方法的准确性，效率和稳定性。
To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and utilizes the fourth-order compact finite difference scheme and matrix transfer technique (MTT) in space with FFT-based implementation. Time integration is done through the accurate fourth-order modified exponential time differencing Runge-Kutta scheme. The linear stability analysis and various numerical experiments including two-dimensional (2D) Fitzhugh-Nagumo, Gierer-Meinhardt, Gray-Scott and three-dimensional (3D) Schnakenberg models are presented to demonstrate the accuracy, efficiency, and stability of the proposed method.
