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Numerical Methods for KdV Type Fractional Order Equation with a Nonlocal Viscous Term

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DOI: 10.23977/icmit.2018.035


Lin Fubiao

Corresponding Author

Lin Fubiao


This paper is to study the numerical solution of the Fractional order equation with a nonlocal viscous term. It proposes a numerical scheme to solve this equation. A detailed analysis is carried out for this scheme, and it is proved 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, the proposed methods are used to investigate the asymptotical decay rate of the solutions to fractional order equation with a nonlocal viscous term. This paper equally discusses the role of the diffusion terms, the geometric dispersion and the nonlinearity respectively. The performed numerical experiment confirms that the decay rates in -norm, -norm,and are very close to-0.25, and -0.5 respectively.


Fractional equation, stability, spectral method, decay rates

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