The purpose of this paper is to test efficiency of the RBF collocation method using approximation by radial basis functions, for solving the classic problem of a meson field. This is a nonlinear evolution problem that uses mixed Crank-Nicolson time discretization scheme and Newton algorithm. Numerical results that prove the convergence and accuracy of the method are given in 2D.

collocation method, radial basis functions (RBFs), approximation, interpolation.