对流扩散方程的紧二次样条配置法  

A Compact Quadratic Spline Collocation Method for the Convection-diffusion Equation

作　　者：罗卫华[1] 

机构地区：[1]内江师范学院数学与信息科学学院//四川省数据恢复重点实验室,四川内江641199

出　　处：《内江师范学院学报》2017年第4期42-46,共5页Journal of Neijiang Normal University

基　　金：四川省教育厅重点项目(15ZA0288)

摘　　要：基于二次样条插值函数,对常系数对流扩散方程提出了一种最优紧配置法.首先在空间方向利用二次样条基函数进行离散,使得问题化为时间方向的一系列常微分方程组;然后,利用Runge-Kutta方法、梯形公式法进行迭代求解,并且在实验中比较、分析了此类配置法在使用Runge-Kutta方法和梯形公式法迭代求解时的数值稳定性.结果表明,在时间方向无论使用哪种迭代法,此配置法在空间方向均可达到4阶精度.Based on the quadratic spline interpolation functions, an optimal compact quadratic spline collocation method is presented for the convection-diffusion equation. As for The said method, first by use of quadratic spline basis function, discret- ization is done in the space direction, thus the problem is transformed into a series of ordinary differential equation. Then, the classical fourth-order Runge-Kutta method and Trapezoid formula are respectively employed to determine the iterative solution and with experiments the numerical stability of the method is compared and analyzed. Numerical examples find that the presen- ted collocation scheme can achieve fourth-order accuracy in space no matter which kind of iterative method is used.

关 键 词：对流扩散方程 二次样条配置法 RUNGE-KUTTA方法 梯形公式 

分 类 号：O241[理学—计算数学]