求解一维对流扩散反应方程的一种隐式差分格式

提出了数值求解一维非稳态对流扩散反应方程的一种隐式差分格式。首先将模型方程利用指数函数转化为对流扩散方程,构造它的差分格式,然后对差分方程的系数进行相应处理,并进行回代,得到对流扩散反应方程的隐式差分格式,其截断误差为O(τ2+h2),采用von Neumann方法证明了格式是无条件稳定的,并且由于每一时间层上只用到了3个网格点,所以可直接采用追赶法求解差分方程,数值结果显示了算法的有效性。

An Implicit Scheme of the 1D Convection-Diffusion-Reaction Equation

An implicit difference scheme is proposed for solving the one-dimensional（1D） unsteady convection-diffusion-reaction equation.By using an exponential function,the model equation can be rewritten in the form of the convection-diffusion equation.Firstly its difference scheme is constructed;then,using the back substitution process,the final implicit scheme is gotten.The truncation of the scheme is O（τ2＋h2）.It is proved to be unconditionally stable by Von Neumann method.Because only three points are used at each time level,the difference equation can be solved by the method of forward elimination and backward substitution.Numerical results indicates the efficiency of the algorithm.