求解对流扩散方程的Pade'逼近格式

The Pade' Approximation Scheme for Solving Convection-Diffusion Equation

对空间变量应用中心差分格式离散,时间变量采用指数函数的Pade'[2/1]逼近,构造了对流扩散方程的精度为O(τ3+h2)的绝对稳定的隐式差分格式,并对其稳定性进行了讨论,将数值实验结果与Crank-Nicholson格式进行比较,验证了文中方法的有效性.

By a central finite difference approximation of second-order for discretizing spatial derivatives and a Pade′[ 2/1 ]approximation method of third-order for the time integration are proposed second-order accuracy in space and third-order accuracy in time for solving convection-diffusion equation. The stability is discussed. Numerical experi-ments are compared with Crank-Nicolson scheme to confirm the validity of the proposed method.