色散方程的一个新的区域分裂并行格式  

A New Domain Decomposition Parallel Scheme for the Dispersive Equation

作　　者：武于佳 朱少红[1] Wu Yujia;Zhu Shaohong(School of Mathematical Sciences,Nankai University,Tianjin 300071,China)

机构地区：[1]南开大学数学科学学院,天津300071

出　　处：《南开大学学报（自然科学版）》2022年第5期50-55,共6页Acta Scientiarum Naturalium Universitatis Nankaiensis

摘　　要：对于色散方程的边值问题提出一个新的区域分裂的并行差分格式,该格式在每一时间层上取三个点作为内边界点,通过显式差分格式计算子域之间内边界点处的近似值,然后,对于各个子域的内点,应用隐格式并行求解.证明了网格比小于3.50时,数值解在离散L_(2)范数意义下关于初值稳定.数值实验验证了理论分析的正确性.A new domain decomposition parallel scheme for the boundary value problem of the dispersive equation is presented.The scheme takes three points as the interface of sub-domains on each time layer,and the interface values is computed by the explicit finite difference formula.Once the interface values are available,the inner values of sub-domains can be computed in parallel by the implicit scheme.The stability about the initial value in the sense of the discrete L_(2) norm is proved under the condition of the grid ratio being less than 3.50.The numerical experiment confirms the correctness of the theoretical analysis.

关 键 词：色散方程 区域分裂 差分格式 稳定性 

分 类 号：O214.82[理学—概率论与数理统计]