RLW方程的有限差分逼近

Finite Difference Approximate Solutions for the RLW Equation

用CrankNicolson格式对RLW方程进行有限差分逼近 ,证明了差分离散方程解的存在唯一性和能量守恒性 ,并对解的误差进行了估计 .最后 ,通过计算验证了解的误差和能量守恒性质 。

In this paper, a finite difference approximation is proposed via Grank Nicolson scheme to solve the regularized long wave (RLW) equations. Existence and uniqueness of numerical solutions are proved. A priori bound and the error estimates as well as conservation of energy of the approximate solutions are discussed in comparison with finite element method.