Abstract
The eigenfunctions of fractional Sturm–Liouville problems (FSLPs) serve as basis functions for the construction of efficient spectral methods for fractional differential equations. In this work, we provide a rigorous error analysis of spectral approximations using eigenfunctions of FSLPs in the uniform norm. Specifically, we first establish bounds on the coefficients in spectral expansions in terms of eigenfunctions of regular and singular FSLPs and then apply these bounds to derive error estimates for spectral approximations in the uniform norm. We also clarify the effect of the parameters in these eigenfunctions on the decay rate of the expansion coefficients. Numerical examples are provided to confirm our analysis.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grant 11671160. The author wishes to thank anonymous reviewers for their helpful comments.
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Wang, H. Analysis of Spectral Approximations Using Eigenfunctions of Fractional Sturm–Liouville Problems. J Sci Comput 81, 1655–1677 (2019). https://doi.org/10.1007/s10915-019-01056-4
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DOI: https://doi.org/10.1007/s10915-019-01056-4