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Numerical Methods for KdV Type Fractional Order Equationwith a Nonlocal Viscous Term(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2020年03期
Page:
28-33
Research Field:
·数学·
Publishing date:

Info

Title:
Numerical Methods for KdV Type Fractional Order Equationwith a Nonlocal Viscous Term
Author(s):
Lin Fubiao1; Ma Lirong2
(1.School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China)(2.Accounting Department,Shijiazhuang Vocational and Technical College of Posts and Telecommunications,Shijiazhuang 050000,China)
Keywords:
fractional equation; stability; spectral method; decay rates
PACS:
O156.5
DOI:
10.3969/j.issn.1001-4616.2020.03.006
Abstract:
We turn to study the numerical solution of the Fractional order equation with a nonlocal viscous term. We propose a numerical scheme to solve this equation. A detailed analysis is carried out for this scheme,and we prove that the scheme is unconditionally stable. The numerical results verify that the fractional order equation with a nonlocal viscous term is of order 1.5,when a nonlocal viscous term does not exist,the scheme is of order 2. At last,we use the proposed methods to investigate the asymptotical decay rate of the solutions to fractional order equation with a nonlocal viscous term. We equally discuss the role of the diffusion terms,the geometric dispersion and the nonlinearity respectively. The performed numerical experiment confirms that the decay rates in L2-norm,L∞-norm,and are very close to -0.25,and -0.5 respectively. These numerical results are consistent with the known theoretical prediction.

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Last Update: 2020-09-15