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A novel meshless collocation solver for solving multi-term variable-order time fractional PDEs
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DOI：10.1007/s00366-021-01298-7.png)
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Abstract
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This paper presents a novel meshless 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 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.
Keywords:
Variable-order time fractional term
Fourier series expansion
Backward substitution method
Collocation method
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