有限差分法和隐式龙格库塔法求解Burgers方程  

Finite Difference Method and Implicit Runge-Kutta Method for Burgers Equation

作　　者：王佩臣[1] 袁海燕[1] 刘鹏[2] 宋玉琦[3] 

机构地区：[1]黑龙江工程学院数学系,哈尔滨150050 [2]黑龙江中医药大学人事处,哈尔滨150008 [3]哈尔滨医科大学公共卫生学院,哈尔滨150001

出　　处：《长春理工大学学报（自然科学版）》2013年第1期158-160,共3页Journal of Changchun University of Science and Technology(Natural Science Edition)

基　　金：黑龙江省自然科学基金(QC2011C020);黑龙江省教育厅科学研究项目(12531546)

摘　　要：提出一个新的方法求解一维Burgers方程,组合使用有限差分法和隐式龙格库塔法求解Burgers方程。首先使用二阶有限差分法进行空间离散,得到一个常微分方程组,然后使用高阶A稳定的隐式龙格库塔法求解常微分方程组,最后比较数值解和精确解,数值结果证实该方法有很高的精度和稳定性。In this paper, we present a new method for solving of the one dimensional Burgers equation, we combined finite difference and implicit Runge-Kutta methods to solve Burgers equation. Firstly, we discretize the Burgers equation. in one dimensional space with 2-order finite difference method, Secondly, we use implicit Runge-Kutta methods for the numerical integration of the system of ODEs. Finally, The numerical results obtained by this way have been compared with the exact solution to show the effcieney of the method. The numerical results demonstrate high accuracy and stability of this method.

关 键 词：有限差分法 隐式龙格库塔法 BURGERS方程 高精度 

分 类 号：O241.82[理学—计算数学]