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A fast finite difference/RBF meshless approach for time fractional convection-diffusion equation with non-smooth solution

机译：具有非平滑解决方案的快速有限差分/ RBF无网格方法分流对流扩散方程

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摘要

In this paper, we propose a fast finite difference/RBF meshless method for time fractional convection-diffusion equation with singularity at the initial moment. Firstly, the time fractional derivative term is discretized by classical L1 format on graded meshes, and the spatial derivative term is approximated by meshless method. The meshless method does not need to construct meshes, which is more conducive for dealing with complex regions or complex boundary conditions. In addition, we adopt proper orthogonal decomposition (POD) technology to derive reduced-order RBF meshless extrapolation algorithm, which effectively reduces the amount of calculation and improves the calculation efficiency. Finally, the accuracy and efficiency of the method are verified by numerical examples.
机译：在本文中，我们在初始时刻提出了一种快速有限差分/ RBF毫无比目扩散方程与奇异性的时间分数对流漫射方程。首先，通过在分级网格上通过经典L1格式离散时间分数衍生项，并且空间导数术语由无网格方法近似。无网格方法不需要构建网状物，这更有利于处理复杂的区域或复杂边界条件。此外，我们采用适当的正交分解（POD）技术来得出降低的RBF无纤维外推算法，其有效地降低了计算量并提高了计算效率。最后，通过数值示例验证了该方法的准确性和效率。

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