Abstract
In the present work, an efficient Lie group integrator called group preserving scheme (GPS) is utilized for the numerical treatment of the Sine-Gordon problems. With the help of a suitable transformation, we turn the main problem into a new one and consequently solve the converted problem using GPS. Indeed, preserving the Lie group structure under discretization has a significant impress on regaining a proper behavior in error minimization. So, by sharing the geometric structure and invariance of the original ODEs, new approaches can be derived, which are more strong, precise, and stable than the conventional numerical methods. Some examples are provided to show the consistency of the approach. Moreover, we construct the conserved vectors (CV) for the governing equation by means of a new theorem of conservation.
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