求解椭圆双曲型奇异摄动问题的一个一致收敛格式  

A Uniformly Convergent Method for a Singularly Perturbed Elliptic-Hyperbolic Equation

作　　者：冯梅[1] 

机构地区：[1]淮安信息职业技术学院基础部,江苏淮安223001

出　　处：《徐州师范大学学报（自然科学版）》2003年第3期6-10,共5页Journal of Xuzhou Normal University(Natural Science Edition)

摘　　要：考察椭圆双曲型奇异摄动问题的数值解法.该方程经过一坐标变换后,可以运用迎风差分格式在均匀网格上直接求解.理论分析和数值结果证明了此时的迎风差分格式是一阶一致收敛的.同时,计算结果表明,应用亏量校正法可得到二阶一致收敛的离散解.A uniformly convergent numerical method is proposed for solving the singular perturbation elliptichyperbolic partial differential equation. By a coordinate transformation, the equation is solved with the upwind difference scheme on an equaldistant mesh. The theoretical analysis and numerical test show that the upwind scheme in this case is uniformly first order convergent. To improve the numerical convergence order, a defect correction method is applied and a discrete solution with uniformly second order convergency is obtained.

关 键 词：椭圆双曲型方程 奇异摄动问题 一致收敛格式 数值解法 迎风差分格式 离散解 亏量校正法 

分 类 号：O175.2[理学—数学] O241.82[理学—基础数学]