非线性RLW方程的特征数值方法

THE CHARACTERISTIC NUMERICAL METHODS FOR NONLINEAR RLW EQUATIONS

如所周知,在孤立子理论的研究及非线性波的物理问题中,RLW(Regularised LongWave)方程占据了相当重要的地位,在非常广泛的领域里得到了应用.因此,对该方程的研究已受到人们的很大重视,有许多专家、学者在这方面已做了不少工作.

The characteristic finite element and finite difference methods (finite element and fini-te difference methods are combined with the method of characteristics) to 1-periodic initial-va-lue problems for the nonlinear RLW (Regularised Long Wave) equations are analyzed. Someoptimal order error estimates and stabilities are obtained for both methods. We report thenumerical results obtained for the solutions of the problems and also compare some of these re-sults with those obtained for finite element, finite difference and spectral schemes.