Abstract
In this paper, we consider the multi-order fractional differential equation and recast it into an integral equation. Based on the integral equation, we develop an hp-version Legendre spectral collocation method and the integral terms with the weakly singular kernels are calculated precisely according to the properties of Legendre and Jacobi polynomials. The hp-version error bounds under the L2-norm and the \(L^{\infty }\)-norm are derived rigorously. Numerical experiments are included to illustrate the efficiency of the proposed method and the rationality of the theoretical results.
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The work was supported by the National Natural Science Foundation of China (Grant No. 12071294) and China Postdoctoral Science Foundation (Grant No. 2020M681345).
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Communicated by: Martin Stynes
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Guo, Y., Wang, Z. An hp-version Legendre spectral collocation method for multi-order fractional differential equations. Adv Comput Math 47, 37 (2021). https://doi.org/10.1007/s10444-021-09858-7
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DOI: https://doi.org/10.1007/s10444-021-09858-7
Keywords
- Multi-order fractional differential equations
- Legendre spectral collocation method
- hp-version error bounds