论文标题
在异常模型中应用的高阶稳健theta方法的构建
Construction of high-order robust theta-methods with applications in anomalous models
论文作者
论文摘要
提出了涉及转移参数$θ$的一般转换策略，以构建分数演算运算符的高阶精度差异公式。通过使用这种策略将二阶向后差公式转换为具有校正项的新型$θ$ -Scheme，它是针对非平滑数据的尺寸扩散问题开发的，即使对于非常小的$α$，这也是可靠的，并且可以解决初始奇异性。最佳误差估计是通过基本参数进行的，并通过数字验证进行了验证。
A general conversion strategy by involving a shifted parameter $θ$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such strategy, a novel $θ$-scheme with correction terms is developed for the subdiffusion problem with nonsmooth data, which is robust even for very small $α$ and can resolve the initial singularity.The optimal error estimates are carried out with essential arguments and are verified by numerical tests.
