High order compact Alternating Direction Implicit method for the generalized sine-Gordon equation

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Abstract

High order compact Alternating Direction Implicit scheme is given for solving the generalized sine-Gordon equation in a two-dimensional rectangular domain. We apply the compact finite difference operators to obtain a fourth order discretization for the second order space derivatives, and we give a linearized three time level algorithm for solving the original nonlinear equation. Error estimate is given by the energy method. Numerical results are provided to verify the accuracy and efficiency of this algorithm.

MSC

65M06
65M12
65M15
35Q51
35Q53
78M20

Keywords

Sine-Gordon equation
High order compact scheme
Alternating Direction Implicit method
Finite difference
Error estimate

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