论文标题
人口动态中空间分数部分微分方程的指数时间差的傅立叶光谱方法
Fourier Spectral Methods with Exponential Time Differencing for Space-Fractional Partial Differential Equations in Population Dynamics
论文作者
论文摘要
管理人口动态的物理定律通常表示为微分方程。近几十年来，研究已将分数阶（非直集）衍生物纳入自然现象的差异模型，例如反应扩散系统。在本文中，我们开发了一种方法来数值求解多组分和多维空间裂缝系统。对于空间离散化，我们采用适合多维PDE系统的傅立叶光谱方法。通过局部一维指数时间差的方法，可以实现有效的时间步变的近似值。我们显示了不同分数参数对生长模型的影响，并考虑了溶液的收敛，稳定性和唯一性，以及参数和边界条件的生物学解释。
Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional-order (non-integer) derivatives into differential models of natural phenomena, such as reaction-diffusion systems. In this paper, we develop a method to numerically solve a multi-component and multi-dimensional space-fractional system. For space discretization, we apply a Fourier spectral method that is suited for multidimensional PDE systems. Efficient approximation of time-stepping is accomplished with a locally one dimensional exponential time differencing approach. We show the effect of different fractional parameters on growth models and consider the convergence, stability, and uniqueness of solutions, as well as the biological interpretation of parameters and boundary conditions.
