论文标题
时间分数微分方程的高阶分级网格方案
Higher order graded mesh scheme for time fractional differential equations
论文作者
论文摘要
在本文中，我们提出了使用分级网格和空间衍生物的标准中心差近似值对Caputo分数（C-F）衍生物的较高近似，以获得时间分数部分微分方程（TFPDE）的近似解。提出的C-F导数近似有效地解决了起源的奇异性，并且很容易适用于各种问题。讨论了拟议方案的稳定性分析和截断误差界限，并分析了解决方案所需的规律性。很少提出数值示例来支持该理论。
In this article, we propose a higher order approximation to Caputo fractional (C-F) derivative using graded mesh and standard central difference approximation for space derivatives, in order to obtain the approximate solution of time fractional partial differential equations (TFPDE). The proposed approximation for C-F derivative tackles the singularity at origin effectively and is easily applicable to diverse problems. The stability analysis and truncation error bounds of the proposed scheme are discussed, along with this, analyzed the required regularity of the solution. Few numerical examples are presented to support the theory.
