Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy
Abstract
We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing the domain into a number of subintervals, and applying the quadratic interpolation on each subinterval. The method is shown to be unconditionally stable, and for general nonlinear equations, the uniform sharp numerical order $3-\nu$ can be rigorously proven for sufficiently smooth solutions at all time steps. The proof provides a general guide for proving the sharp order for higher-order schemes in the nonlinear case. Some numerical examples are given to validate our theoretical results.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2020
- DOI:
- 10.48550/arXiv.2002.09733
- arXiv:
- arXiv:2002.09733
- Bibcode:
- 2020arXiv200209733C
- Keywords:
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- Mathematics - Numerical Analysis