二阶双曲型方程的精细时程积分法  

On precise time-integration method for second order hyperbolic differential equations

作　　者：金承日[1] 吕万金[2] 

机构地区：[1]哈尔滨工业大学威海分校理学系,山东威海264209 [2]黑龙江大学理学院,哈尔滨150080

出　　处：《计算力学学报》2003年第1期113-115,共3页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(60074015);哈尔滨工业大学(威海)校科学研究基金资助项目(2000-15;14).

摘　　要：对于二阶双曲型偏微分方程初边值问题,可以用有限差分法进行求解。通常的有限差分法在使用过程中受到精确度和稳定性的限制,本文提出求解二阶双曲型方程的精细时程积分法。由于这种方法是半解析方法,在时间域上可以精确计算,所以这种方法不仅精确度高,而且还绝对稳定。文末的数值算例进一步验证了上述结论,而且对大的时间步长(例如Δt=0.5)仍然获得精度很高的数值结果。可见,精细时程积分法是一种很实用的方法。The initial boundary value problem of the second order hyperbolic partial differential equations can be solved by using finite difference method.However, the usual finite difference method faces the problems of numerical stability and precision, the precise time\|integration method is proposed for the second order hyperbolic differential equations in this paper.The method is a semi\|analytical method, hence it can be accurately solved on time domain and it has accurate and absolutely stable.The numerical example shows that the method has high accuracy even for very large time\|step sizes(e.g.Δt=0.5) and good practicability.

关 键 词：双曲型方程 精细时程积分法 精确度 稳定性 

分 类 号：O241.8[理学—计算数学]