An implicit Lie-group iterative scheme for solving the nonlinear Klein-Gordon and sine-Gordon equations

In this article, the nonlinear Klein-Gordon and sine-Gordon equations are solved by pondering the semi-discretization numerical schemes and then, the resulting ordinary differential equations at the discretized spaces are numerically integrated toward the time direction by using the implicit Lie-group iterative method to find the unknown physical quantity. When six numerical experiments are examined, we reveal that the present implicit Lie-group iterative scheme is applicable to the nonlinear Klein-Gordon and sine-Gordon equations and convergent very fast at each time marching step, and the accuracy is raised several orders, of which the numerical results are rather accurate, effective and stable. (C) 2015 Elsevier Inc. All rights reserved.