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

2020/07/18 by Tian Xia, Tian, Xia, Sergiy Reutskiy +3
Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2007.09535

openalex publication_date 2020/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Fractional Brownian Motions, Fractional Noises and Applications

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