一类广义Boussinesq方程的守恒差分格式  

A conservation of difference scheme for a class of generalized Boussinesq equation

作　　者：姜晓丽 JIANG Xiaoli(College of Mathematics and Physics, Bohai University, Jinzhou 121013 , China)

机构地区：[1]渤海大学数理学院,锦州121013

出　　处：《黑龙江大学自然科学学报》2019年第1期27-33,共7页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11101102);辽宁省百千万人才计划基金项目(2013921055);辽宁省博士启动基金项目(20141139)

摘　　要：研究一类六阶广义Boussinesq方程的数值算法,方程中包含多项高阶色散项,模型形式和非线性都很复杂。从定性分析的角度给出数值解的几种性质,设计一种基于待定系数法的能量守恒差分格式,对高阶色散和非线性源的差分形式进行了恰当的处理。结果表明,设计的有限差分法能有效地找到复杂结构项的差分形式,得到较好的收敛阶;讨论分析了数值解的稳定性和存在性。The numerical algorithm of a class of six order generalized Bq equations is researched, and several properties of the numerical solution are given qualitatively. Here, high order dispersion terms in the equations make the nonlinear effect and the pattern of model complicated. A finite difference method with undetermined coefficients for energy conservation format is presented, and differential forms for high-order dispersion and nonlinear source is properly dealt with. The results show that this method of the differential form with complex structure can be found effectively, and its good convergent order can be given. The stability and existence of the numerical solutions are discussed and analyzed.

关 键 词：广义BOUSSINESQ方程 守恒差分格式 稳定性 收敛性 

分 类 号：O241.8[理学—计算数学]