Burgers-KdV方程差分解的收敛性和稳定性

The Convergence and Stability of Differential Solutions for Burgers-KdV Equation

对 Burgers- Kd V方程的周期边值问题建立了全离散两层加权中心差分格式 ,得到差分解及其高阶差商的模估计 ,从而证明了差分解的收敛性和稳定性 ,并且得到了显格式和弱隐格式收敛性及稳定性的步长限制条件 .

In this paper,we construct the full-discrete center differential schemes with a parameter α for the periodic boundary problem of the Burgers-KdV equation.The estimates of the differential solution and its differential quotient of high order are obtained.The convergence and the stability of differential solutions are proved. Especially the restriction conditions to the steplength for the explicit and weakly implicit schemes are found.