G. Berikelashvili and M. Mirianashvili ON A THREE LEVEL DIFFERENCE SCHEME FOR THE REGULARIZED LONG WAVE EQUATION

We consider an initial boundary-value problem for the Regularized Long Wave equation. A three level conservative difference scheme is studied. On the first level a two level scheme is used to find the values of the unknown functions which ensures the expression of the initial energies only by the initial data. The obtained algebraic equations are linear with respect to the values of the unknown function for each new level. The use of the Gronwall lemma does not require any restriction on mesh steps. It is proved that the finite difference scheme converges with the rate O(τ 2 +h) when the exact solution belongs to the Sobolev space W 3 2 . ! " # $ % " $ " % $ # % % " # & # ! " ! O(τ + h) ' " ! W 3 2 # 2000 Mathematics Subject Classification: 65M06, 35L70.