Abstract
Purpose: This paper studies the Phi-four equation that appears in relativistic quantum mechanics. The primary purpose of this paper is to address the numerical simulations of this model.
Methods: The singular soliton solution is also obtained by the ansatz method.
Results: The constraint conditions are indicated for the existence of the soliton. Numerical solutions are obtained by using the spectral method where rational Chebyshev functions are used as basis functions.
Conclusions: Results are validated by finding error estimates.