高阶椭圆型偏微分方程奇异摄动问题一致收敛差分格式  

A Uniformly Convergent Difference Scheme for the Singular Perturbation Problem of a High Order Elliptic Differential Equation

作　　者：刘国庆[1] 苏煜城[1] 

机构地区：[1]南京化工学院,南京大学

出　　处：《应用数学和力学》1996年第5期397-404,共8页Applied Mathematics and Mechanics

摘　　要：本文，我们讨论了一类高阶椭圆型偏微分方程奇异摄动问题．给出了连续问题解的先验估计．另外，我们还提供了一种数值求解该类问题的指数型差分格式．最后，证明了差分问题的解在能量范数意义下关于小参数一致收敛到连续问题的解．In this paper, we first consider the singularly Perturbed boundary value problem for the fourth-order elliptic di fferential equation, estaqlish the priori estimation of the solution of the continuous problem. Then, we present an exponential fitted difference scheme and discuss the selution properties of the di fference equations. Finally, the uniform convergence of this scheme with respect to the small parameter in the ediscrete energy norm, is proved.

关 键 词：差分格式 一致收敛 椭圆型方程 奇摄动 边值问题 

分 类 号：O241.82[理学—计算数学]