An Implicit Scheme of Lattice Boltzmann Method for Sine-Gordon Equation

We establish an implicit scheme of lattice Boltzmann method for simulating the sine-Gordon equation, which can be transformed into the explicit one, so the computation of the scheme is simple. Moreover, the parameter θ of the
implicit scheme is independent of the relaxation time, which makes the model more flexible. The numerical results show that this method is very effective.