求解广义BBM-Burgers方程的一个两层非线性守恒差分格式

摘要

对广义BBM-Burgers方程的初边值问题进行了数值研究，提出一个两层非线性Crank-Nicolson差分格式，格式合理地模拟方程本身的一个守恒量，得到差分解的先验估计和存在唯一性，并利用能量方法分析该格式的二阶收敛性与无条件稳定性。%In this paper, a two level nonlinear Crank-Nicolson difference scheme is proposed. The scheme provides a numerical solution to the initial boundary value problem of general BBM-Burgers equation. A conservative variable of the equation is simulated well with the scheme. In the simulation, the prior estimate and uniqueness of the solution are also obtained. In addition, the second or-der convergence and unconditional stability are proved by using energy analysis.