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首页> 外文会议>Proceedings of the Fifth symposium on fractional differentiation and its applications >An implicit RBF meshless method for a fractal mobile/immobile transport model
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An implicit RBF meshless method for a fractal mobile/immobile transport model

机译：分形移动/不移动运输模型的隐式RBF无网格方法

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摘要

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.
机译：分数阶微分方程用于描述具有幂律记忆功能的移动/不动运输的分形模型。该方程式是控制连续时间随机游走和重尾随机等待时间的极限方程。在本文中，我们首先提出了一种有限差分方法来离散时间变量并获得一个半离散方案。然后我们讨论其稳定性和收敛性。其次，我们考虑基于径向基函数（RBF）的无网格方法离散化空间变量。与传统的FDM和FEM相比，无网格方法具有明显的优势：可以独立于网格进行计算，更精确，并且可以用于解决复杂的问题。最后，通过数值算例验证了收敛阶，描述了具有不同问题域的移动/不固定运输过程的分形模型。数值结果表明，本发明的无网格方法对于分数阶微分方程的建模和仿真非常有效，并且对于开发由各种类型的分数阶微分方程控制的工程和科学问题的鲁棒仿真工具具有良好的开发潜力。

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