SYMPLECTIC SCHEMES FOR TELEGRAPH EQUATIONS

作     者：Yi Lu Yaolin Jiang 

作者机构：School of Mathematics and Statistics Xi'an Jiaotong University Shaanxi 710049 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2016年第34卷第3期

页      面：285-299页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：Acknowledgments. This work is supported by the Natural Science Foundation of China (NSFC) under grant 11371287 and the International Science and Technology Cooperation Program of China under grant 2010DFA14700 

主　　题：Telegraph equation Klein-Gordon equation Symplectic method Explicitmethod. 

摘      要：A new numerical algorithm for telegraph equations with homogeneous boundary con- ditions is proposed. Due to the damping terms in telegraph equations, there is no royal conservation law according to Noether＇s theorem. The algorithm origins from the discovery of a transform applied to a telegraph equation, which transforms the telegraph equation to a Klein-Gordon equation. The Symplectic method is then brought in this algorithm to solve the Klein-Gordon equation, which is based on the fact that the Klein-Gordon equation with the homogeneous boundary condition is a perfect Hamiltonian system and the symplectic method works very well for Hamiltonian systems. The transformation itself and the inverse transformation theoretically bring no error to the numerical computation. Therefore the error only comes from the symplectic scheme chosen. The telegraph equation is finally explicitly computed when an explicit symplectic scheme is utilized. A relatively long time result can be expected due to the application of the symplectic method. Mean- while, we present order analysis for both one-dimensional and multi-dimensional cases in the paper. The efficiency of this approach is demonstrated with numerical examples.