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Mathematical Problems in Engineering
Volume 2015, Article ID 548905, 11 pages
Research Article

Numerical Approximation of Nonlinear Klein-Gordon Equation Using an Element-Free Approach

College of Information Technology, Shanghai Ocean University, Shanghai 201306, China

Received 1 July 2014; Accepted 22 August 2014

Academic Editor: Kim M. Liew

Copyright © 2015 Dong-mei Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Numerical approximation of nonlinear Klein-Gordon (KG) equation with quadratic and cubic nonlinearity is performed using the element-free improved moving least squares Ritz (IMLS-Ritz) method. A regular arrangement of nodes is employed in this study for the numerical integration to compute the system equation. A functional formulation for the KG equation is established and discretized by the Ritz minimization procedure. Newmark’s integration scheme combined with an iterative technique is applied to the resulting nonlinear system equations. The effectiveness and efficiency of the IMLS-Ritz method for the KG equation have been testified through convergence analyses and comparison study between the present results and the exact solutions.