An efficient high order numerical scheme for the time-fractional diffusion equation with uniform accuracy
An efficient high order numerical scheme for the time-fractional diffusion equation with uniform accuracy
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DOI：
10.3934/math.2023818
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发表时间：
2023
期刊：
影响因子：
2.2
通讯作者：
Junying Cao;Qing Tan;Zhong-qing Wang;Ziqiang Wang
中科院分区：
文献类型：
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作者：
Junying Cao;Qing Tan;Zhong-qing Wang;Ziqiang Wang
构造具有一致收敛阶的时间分数阶扩散方程数值格式是一个重要的研究课题。我们致力于研究一个有效的统一精度计划的TFDES。首先，我们利用分段二次插值构造了时间分数阶导数的一个有效的一致精度格式。并给出了有效格式的局部截断误差。其次，将空间中心二阶格式与上述有效时间格式相结合，给出了时间离散方程的全离散数值格式。第三，对有效格式的稳定性和误差估计进行了严格的理论分析，得到了无条件稳定格式在时间上具有3-beta收敛阶和一致精度。最后，数值算例表明该格式是一个有效的无条件稳定格式。
The construction of efficient numerical schemes with uniform convergence order for time-fractional diffusion equations (TFDEs) is an important research problem. We are committed to study an efficient uniform accuracy scheme for TFDEs. Firstly, we use the piecewise quadratic interpolation to construct an efficient uniform accuracy scheme for the fractional derivative of time. And the local truncation error of the efficient scheme is also given. Secondly, the full discrete numerical scheme for TFDEs is given by combing the spatial center second order scheme and the above efficient time scheme. Thirdly, the efficient scheme's stability and error estimates are strictly theoretical analysis to obtain that the unconditionally stable scheme is $ 3-\beta $ convergence order with uniform accuracy in time. Finally, some numerical examples are applied to show that the proposed scheme is an efficient unconditionally stable scheme.