Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein–Gordon equation

This paper aims to obtain approximate solutions of the Nonlinear Klein–Gordon (NLKG) equation by employing the Boundary Integral Equation (BIE) method and the Dual Reciprocity Boundary Element Method (DRBEM). This method is improved by using a predictor–corrector scheme to the nonlinearity which appears in the problem. We employ the time stepping scheme to approximate the time derivative, and the Linear Radial Basis Functions (LRBFs), are used in the Dual Reciprocity (DR) technique. To confirm the accuracy of the new approach, the numerical results of a Double-Soliton and a problem with inhomogeneous terms are compared with analytical solutions and for the examples possessing single and periodic waves, two conserved quantities associated to the (NLKG) equation, the energy and the momentum are investigated.