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arXiv · 2007.09535

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

Xia Tian·S. Yu. Reutskiy·Zhuo-Jia Fu
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Abstract

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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Xia Tian, S. Yu. Reutskiy, Zhuo-Jia Fu. 2020-07-18. A semi-analytical collocation method for solving multi-term variable-order time fractional partial differential equations. https://arxiv.org/abs/2007.09535

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