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HIGH-ORDER SOLVERS FOR SPACE-FRACTIONAL DIFFERENTIAL EQUATIONS WITH RIESZ DERIVATIVE

机译：具有RIESZ衍生物的空间分数微分方程的高阶求解器

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摘要

This paper proposes the computational approach for fractional-in-space reaction-diffusion equation, which is obtained by replacing the space second-order derivative in classical reaction-diffusion equation with the Riesz fractional derivative of order αin (0, 2]. The proposed numerical scheme for space fractional reaction-diffusion equations is based on the finite difference and Fourier spectral approximation methods. The paper utilizes a range of higher-order time stepping solvers which exhibit third-order accuracy in the time domain and spectral accuracy in the spatial domain to solve some fractional-in-space reaction-diffusion equations. The numerical experiment shows that the third-order ETD3RK scheme outshines its third-order counterparts, taking into account the computational time and accuracy. Applicability of the proposed methods is further tested with a higher dimensional system. Numerical simulation results show that pattern formation process in the classical sense is the same as in fractional scenarios.
机译：本文提出了分级空间反应扩散方程的计算方法，通过用αin（0,2]的riesz分数衍生物在古典反作用扩散方程中替换空间二阶衍生物来获得。提出的空间分数反应扩散方程的数值方案基于有限差分和傅里叶谱近似方法。该纸利用一系列高阶时间踩踏求解器，其在时域中展示了三顺精度和空间域中的光谱精度解决一些分数空间反应扩散方程。数值实验表明，三阶ETD3RK方案占据其三阶对应物，考虑到计算时间和准确性。所提出的方法的适用性进一步测试了高尺寸系统。数值模拟结果表明，经典意义上的模式形成过程是山姆E作为分数方案。

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