Abstract
In this paper, we propose and analyze a fractional spectral method for the time-fractional diffusion equation (TFDE).
The main novelty of the method is approximating the solution by using a new class of generalized fractional Jacobi
polynomials (GFJPs), also known as Müntz polynomials.
We construct two efficient schemes using GFJPs for TFDE: one is based on the Galerkin formulation
and the other on the Petrov–Galerkin formulation.
Our theoretical or numerical investigation shows that both schemes are exponentially convergent
for general right-hand side functions, even though the exact solution has very limited regularity (less than
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11471274
Award Identifier / Grant number: 11421110001
Award Identifier / Grant number: 51661135011
Award Identifier / Grant number: 91630204
Funding statement: This research is partially supported by the National Natural Science Foundation of China (grant numbers 11471274, 11421110001, 51661135011, and 91630204).
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