Iterative implicit schemes for the two- and three-dimensional Sine—Gordon equation

摘要

In this paper, ring wave solutions to the Sine—Gordon equation urr + {(m − 1)/r}ur − utt = sin u, in two and three dimensions are investigated by numerical computations. The combined approach of linearization and finite differences is used to get iterative implicit schemes for solving the Sine—Gordon equation. The accuracy and efficiency of the schemes are discussed. The numerical results show that each expanding wave exhibits a return effect. Collision experiments for expanding and shrinking concentric ring waves are carried out. The results show that the solutions possess quasi soliton properties.