A numerical algorithm of solving the forced sine-Gordon equation

The numerical method of solving the problem of small perturbations of a stationary traveling solution (soliton) of well-known in physics sin-Gordon equation is presented. The solution is reduced to solving a set of linear hyperbolic partial differential equations. The Riemann function method is used to find a solution of a linear PDE. The value of the Riemann function at any particular point is found as a solution of an ordinary differential equation. An algorithm of calculation of a double integral over a triangular integration area is given.