论文标题

一种半分析搭配方法,用于求解多项可变时间分数部分微分方程

A semi-analytical collocation method for solving multi-term variable-order time fractional partial differential equations

论文作者

Tian, Xia, Reutskiy, S. Yu., Fu, Zhuo-Jia

论文摘要

本文提出了一种新型的半分析搭配方法,用于求解多项可变时间分数偏微分方程(fotfpdes)。在提出的方法中,它采用了傅立叶系列扩展进行空间离散化,该扩展将原始的多项cotfpdes转换为一系列多项可变时间分数分数普通微分方程(votfodes)。然后,可以使用最近开发的向后替换方法来解决这些投票。几个数值示例验证了拟议的数值方法在多项cotfpdes解决方案中的准确性和效率。

This paper presents a novel semi-analytical collocation method to solve multi-term variable-order time fractional partial differential equations (VOTFPDEs). In the proposed method it employs the Fourier series expansion for spatial discretization, which transforms the original multi-term VOTFPDEs into a sequence of multi-term variable-order time fractional ordinary differential equations (VOTFODEs). Then these VOTFODEs can be solved by using the recent-developed backward substitution method. Several numerical examples verify the accuracy and efficiency of the proposed numerical approach in the solution of multi-term VOTFPDEs.

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