用修正Bernstein多项式Galerkin法求KdV-Burgers方程数值解

摘要

采用修正Bernstein多项式作为基函数,使用Galerkin逼近,构造了数值求解KdV-Burgers方程的隐式格式.该格式具有很好的数值稳定性,能够有效处理长时间演化问题,数值解具有高精度.%An implicit scheme of solving numerical solution of KdV-Burgers' equation is constructed by applying modified Bernstein polynomials as basis function and Galerkin approximation. The scheme is of well numerical stability, and effective for long time evolution behavior. The numerical results are in well agreement with the exact solutions.