Fully discrete spectral methods for solving time fractional nonlinear Sine–Gordon equation with smooth and non-smooth solutions

作者：

Highlights：

• A time fractional nonlinear Sine–Gordon equation is considered.

• Legendre spectral approximation in space is proposed.

• The discretization in time for smooth and non-smooth solutions.

• The stability and convergence are analysed.

• Numerical experiments are presented to confirm our theoretical analysis.

摘要

•A time fractional nonlinear Sine–Gordon equation is considered.•Legendre spectral approximation in space is proposed.•The discretization in time for smooth and non-smooth solutions.•The stability and convergence are analysed.•Numerical experiments are presented to confirm our theoretical analysis.

论文关键词：Time fractional nonlinear Sine–Gordon equation,Legendre spectral method,Stability and convergence,Caputo derivative,Smooth and non-smooth solutions

论文评审过程：Received 17 April 2017, Revised 12 March 2018, Accepted 14 March 2018, Available online 12 April 2018, Version of Record 12 April 2018.

论文官网地址：https://doi.org/10.1016/j.amc.2018.03.069