非线性对流反应扩散方程的预估-校正单调迭代差分方法

The Prediction-Correction Monotone Finite Difference Methods for Nonlinear Transport-Diffusion Equations

考虑了一维非线性对流反应扩散方程,建立了求解该方程的预估-校正单调迭代差分方法,并用构造上下解序列的技巧建立了单调迭代算法.该方法在时空方向分别具有2阶和4阶精度,数值结果显示了算法的有效性.

The one-dimension nonlinear transport-diffusion equations were considered. The monotone finite difference and corresponding prediction-correction methods were proposed. The monotone iterative algorithms were achieved by using the superior and inferior numerical solution sequences. It was shown that the numerical solution possesses the second order in time and the fourth order in space. The algorithms are supported by the numerical results efficiently.