Crank-Nicolson Legendre spectral approximation for space-fractional Allen-Cahn equation
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Date
2019-05-31
Authors
Chen, Wenping
Lu, Shujuan
Chen, Hu
Liu, Haiyu
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we consider spectral methods for solving the initial-boundary value problem of the space fractional-order Allen-Cahn equation. A fully discrete scheme based on the modified Crank-Nicolson scheme in time and the Legendre spectral method in space is established. The existence and uniqueness of the fully discrete scheme are derived, and the stability and convergence analysis of the fully discrete scheme are proved rigorously. By constructing a fractional duality argument, the corresponding optimal error estimates in L2 and Hα norm are derived, respectively. Also, numerical experiments are performed to support the theoretical results.
Description
Keywords
Space-fractional Allen-Cahn equation, Legendre spectral method, Modified Crank-Nicolson scheme, Stability, Convergence
Citation
Chen, W., Lu, S., Chen, H., & Liu, H. (2019). Crank-Nicolson Legendre spectral approximation for space-fractional Allen-Cahn equation. <i>Electronic Journal of Differential Equations, 2019</i>(76), pp. 1-17.