Kdv-Burgers方程的两层线性化隐式差分格式

A two-level and linearized implicit difference scheme for the Kdv-Burgers' equation

应用非线性对流项和反应项的两层线性化技巧,对非线性Kdv-Burgers方程周期边界问题构建了一类具有二阶截断误差的两层线性化隐式差分格式.用数学归纳原理和离散能量法建立了差分格式的唯一可解性、在最大模意义下的收敛性和稳定性.数值计算表明,该格式在时间和空间上都是二阶收敛的.

Based on two-level linearized technique for nonlinear convection and reaction term, a twolevel linearized implicit difference scheme with second-order truncation error is presented for the periodic boundary problem of nonlinear Kdv-Burgers equations. The unique solvability, convergence and stability in the maximum norm of difference scheme are obtained by mathematical induction and discrete energy methods. It is shown by numerical experiments that the scheme is second- order convergent in both space and time.