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.
翻译:在本条中,我们建议使用空间衍生物的分级网格和标准中央差差差近近近法,对卡普托分数衍生物(C-F)的衍生物(C-F)进行更高的排序近似,以获得时间分数部分差异方程(TFPDE)的近近近似法。C-F衍生物的拟议近似法有效地解决了原产地的独一性,并且很容易适用于各种问题。讨论了拟议办法的稳定性分析和截断误差界限,同时分析了解决办法的常规性。几乎没有数字例子支持这一理论。