Givi Berikelashvili, Nodar Khomeriki and Manana Mirianashvili

On the Convergence Rate Analysis of One Difference Scheme for Burgers' Equation

abstract:
We consider an initial boundary value problem for the 1D nonlinear Burgers' equation. A~three-level finite difference scheme is studied. Two-level scheme is used to find the values of unknown function on the first level. The obtained algebraic equations are linear with respect to the values of the unknown function for each new level. It is proved that the scheme is convergent at rate $O(\tau^{k-1}+h^{k-1})$ in discrete $L_2$-norm when an exact solution belongs to the Sobolev space $W_2^k$, $2<k\leq 3$.

Mathematics Subject Classification: 65M06, 65M12, 76B15

Key words and phrases: Burgers' equation, difference scheme, convergence rate.