【摘要】 首先,针对一维对流扩散反应方程,借助截断误差余项修正的方法,将中心差分格式余项中未知函数的三阶和四阶导数项利用一阶导数的表达式来代替,从而提出一种新的紧致差分格式,具有四阶精度.然后,为了简化计算,对格式常系数形式的耗散误差和色散误差进行分析,证实该格式的低耗散性.接着,将该方法推广到二维,运用降维的思想转化成2个一维形式的定常对流扩散反应方程,并用求解一维方程的方法,离散后相加即得二维对流扩散反应方程的紧致差分格式.最后,通过数值实验验证本文格式的精确性和可靠性.更多还原

【Abstract】 In this paper,by means of truncation error remainder correction method,the third and fourth order derivative terms of unknown functions in the truncation error remainder in the central difference scheme are replaced by the expressions of the first order derivatives. A new compact difference scheme with four order accuracy is proposed for solving the one-dimensional convection diffusion reaction equation. To simplify,the dissipation and dispersion errors of constant coefficient schemes are analyzed to show the low dissipation. Then,extending this method to the two-dimensional case,the two-dimensional equation is transformed into two one-dimensional steady convection diffusion reaction equations with the thought of reducing dimensions which can be solved by the method for the onedimensional equation. Lastly,numerical experiments are given to verified the accuracy and reliability of the present scheme.更多还原