数值求解对流方程的一族三阶精度差分格式  

A Group of Difference Schemes with 3^(rd)-Order Accuracy for Solving Convective Equations

作　　者：杨祖华[1] 张大凯[2] 龙超云[1] 肖勇军[1] 王志平[1] 

机构地区：[1]贵州大学理学院物理系,贵阳550025 [2]贵州大学理学院数学系,贵阳550025

出　　处：《西南大学学报（自然科学版）》2009年第5期6-12,共7页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60666001);贵州省优秀科技青年计划培养基金资助项目(2002No.2013)

摘　　要：在6个节点基础上应用组合差商方法构造了求解对流方程的一类差分格式,该类差分格式包括了一个隐式差分格式和一个半显差分格式,这两个格式均由包括6个节点的两组线性无关的差商构成,具有精度高、相对误差很小、计算简单、工作量少、编程简便等优美特点.详细地分析了差分格式的稳定性,给出了两个数值实例,并对实例中的误差做了图表展示.A new group of compact difference schemes containing three parameters of the third order is giv en for the difference convection problems with constant coefficient. These difference schemes contain an implicit scheme and a semi-significant difference scheme. Both schemes consist of two difference quo tients, each containing 6 nodal points. This method is characterized by high accuracy, small relative error [their truncation error is as low as O（τ^3 ＋h^3 ）], simplicity in calculation, low workload and convenience in writing programs. The scheme is applicable for solving convective equations with constant coefficients.

关 键 词：对流方程 三阶精度 差分格式 

分 类 号：O241.1[理学—计算数学]