无界区域上耦合sine-Gordon方程组的分裂局部人工边界条件  

Splitting local artificial boundary conditions for coupled sine-Gordon equations on unbounded domains

作　　者：谢冰[1] 台怡农 李宏伟 XIE Bing;TAI Yinong;LI Hongwei(Jinan Yuying Middle School,Jinan 250001,China;School of Mathematics and Statistics,Shandong Normal University,Jinan 250358,China)

机构地区：[1]济南育英中学,山东济南250001 [2]山东师范大学数学与统计学院,山东济南250358

出　　处：《齐鲁工业大学学报》2024年第4期72-80,共9页Journal of Qilu University of Technology

基　　金：山东省自然科学基金资助项目(ZR2019BA002)。

摘　　要：研究了在等离子体物理学中有广泛应用的无界区域上耦合sine-Gordon方程组的数值解法,由于物理区域的无界性和方程组的非线性,使得常用的数值方法不能直接用于求解此问题。利用人工边界方法和算子分裂方法设计了合理的分裂局部人工边界条件,解决了物理区域的无界性和方程组的非线性给数值计算带来的困难。无界区域上的Cauchy问题简化为有界区域上的初边值问题,从而可以利用有限差分方法进行数值求解。最后,通过数值算例验证了所设计边界条件的精确性和有效性,并模拟了多孤立波的传播。This paper aims to study the numerical solution of the coupled sine-Gordon equations on an unbounded domain,which is widely applied in plasma physics.The unboundedness of the physical domain and the nonlinearity of the equations make it challenging to derive the numerical solution.Employing the artificial boundary method and the operator splitting approach to overcome the unboundedness and nonlinearity,the splitting local artificial boundary method was established for the coupled sine-Gordon equations.The Cauchy problem was reduced into an initial boundary value problem on a bounded computational domain,which can be efficiently solved by the finite difference method.The accuracy and effectiveness of the proposed method were demonstrated by some numerical results,and the propagation of solitons was simulated.

关 键 词：耦合sine-Gordon方程组 人工边界方法 算子分裂方法 无界区域 有限差分法 

分 类 号：O241.82[理学—计算数学]