A one-parameter family of difference schemes for the regularized long-wave equation

作者：Berikelashvili Givi^*; Mirianashvili Manana

来源：Georgian Mathematical Journal, 2011, 18(4): 639-667.

DOI：10.1515/GMJ.2011.0044

• Finite difference scheme
• convergence rate
• regularized long-wave equation
• artificial boundary conditions
• solitary wave collisions
• mass transfer
• numerical results

We consider an initial boundary-value problem for the regularized long-wave equation. A three level one-parameter family of conservative difference schemes is studied. Two level schemes are used to find the values of the unknown functions on the first level. A numerical method for selection of artificial boundary conditions is proposed. It is proved that the finite difference scheme converges at rate O(tau(2) + h(2)) when an exact solution belongs to the Sobolev space W-2(3).

• 出版日期2011