Study of quasi-wavelet based numerical method applied to nonlinear Klein-Gordon equations

A new quasi-wavelet method is introduced for solving the nonlinear Klein-Gordon (NKG) equations which are very important to relativistic quantum mechanics and other mathematics and physics problems. On the one hand, the quasi-wavelet method is utilized to discretize the spatial derivatives, On the other hand, the fourth-order Runge-Kutta scheme is employed for the temporal discretization. The quasi-wavelet solutions are well consistent with the asymptotic solutions obtained by a modified Lindstedt-Poincare (MLP) method. Numerical results indicate that the quasi-wavelet approach is very robust and efficient in solving nonlinear partial differential equations.