提出一种消除对流扩散反应方程中对流项的处理技巧,结合中心差分格式的新方法与相同节点的迎风差分格式相比具有更好的精度,该方法很容易与Pad6格式相结合,构造出具有四阶精度的无条件稳定的高阶差分格式.数值实验表明,新方法具有很好的精度和健壮性,并且可以有效求解对流占优问题.
A method to eliminate the convection term from convection diffusion reaction equations ;s presented in this paper. The new method, combined with the central difference schemes, can achieve better accuracy than the upwind schemes on the same finite difference stencil. It can also be easily combined with the Pad4 approximation to achieve fourth-order accuracy, and unconditional stability is also proved. Numerical examples involving one dimensional equations is presented in the paper to demonstrate the accuracy and robustness of the new approaches and they can effectively solve the convection dominate problems.