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

作者：Chang Chih Wen^*; Liu Chein Shan

来源：Applied Mathematical Modelling, 2016, 40(2): 1157-1167.

DOI：10.1016/j.apm.2015.06.028

• Nonlinear Klein-Gordon equation
• Sine-Gordon equation
• Nonlinear wave problem
• Implicit Lie-group iterative scheme
• Group preserving scheme (GPS)

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.

• 出版日期2016-1-15