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A new linearized difference scheme for time fractional regularized long wave equation
  • Xinlong Liu,
  • Lifei Wu,
  • Xiaozhong Yang
Xinlong Liu
North China Electric Power University
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Lifei Wu
North China Electric Power University
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Xiaozhong Yang
North China Electric Power University

Corresponding Author:[email protected]

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Abstract

Fractional regularized long wave (FRLW) equation describes various physical phenomena in ocean engineering, such as long wave and shallow water wave with small amplitude, the study of its numerical solution has important theoretical significance and application value. A new linearized difference scheme is proposed for Caputo type time fractional regularized long wave (TFRLW) equation. The time direction discretization of the scheme adopts L1 approximation of piecewise linear interpolation, and the space direction discretization is based on the linearization of the nonlinear term of TFRLW equation. The existence and uniqueness of the solution of the difference scheme are proved, and the stability and convergence of the scheme are proved by the discrete energy method. The analysis results show that the new scheme has spatial accuracy of 2 order and time accuracy of order. Finally, numerical experiments verify the correctness of the theoretical analysis and the effectiveness of the numerical scheme.