期刊
COMPUTATIONAL & APPLIED MATHEMATICS
卷 40, 期 8, 页码 -出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s40314-021-01657-6
关键词
Time-fractional KdV equation; Caputo fractional derivative; L2-1(sigma) method; Weak singularity; Grade mesh
资金
- NSF of China [11771060, 11371302]
- Scientific Research Fund of Hunan Provincial Education Department, China [18C0809]
- Science and technology planning project of Shaoyang science and Technology Bureau [2020GZ88]
- Shanghai Science and Technology Planning Projects [20JC1414200]
- Natural Science Foundation of Shanghai [20ZR1441200]
An efficient numerical method is proposed for the nonlinear time fractional KdV equation with Caputo fractional derivative, which can effectively handle the weak singularity of the model at t = 0 and has high accuracy. The stability and convergence of the difference scheme are rigorously established, supported by several numerical experiments.
In this paper, an efficient numerical method is proposed for the nonlinear time fractional Korteweg-de Vries (KdV) equation with Caputo fractional derivative of order alpha is an element of (0, 1). The scheme is based on a nonuniform L2-1(sigma) formula in time and a second-order finite difference in space. The numerical method can not only effectively deal with the weak singularity of the fractional model at t = 0, but also has high accuracy. The stability and convergence of the difference scheme are rigorously established. Finally, several numerical experiments are provided to support the theoretical results.
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