Abstract
Firstly, we show the uniqueness and existence of the weak solution of the nonlocal model, and study the local limit of the nonlocal model as horizon parameters approach zero. Particularly, it is shown that the convergence is uniform at a rate of O(δ+σ2), under certain regularity assumptions on initial and source data. Next we propose a fully discrete scheme, by exploiting the quadrature-based finite difference method in time and the Fourier spectral method in space, and show its stability. The numerical scheme is proved to be asymptotically compatible so that it preserves the local limiting behavior at the discrete level. Numerical experiments are provided to illustrate the theoretical results.
Original language | English |
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Pages (from-to) | 361-371 |
Number of pages | 11 |
Journal | Chaos, Solitons and Fractals |
Volume | 102 |
DOIs | |
Publication status | Published - 1 Sept 2017 |
Externally published | Yes |
Keywords
- Asymptotically compatibility
- Fourier spectral method
- Local limit
- Quadrature-based finite difference
- Space-time nonlocal equation
- Well-posedness
ASJC Scopus subject areas
- General Mathematics