No abstract

In this article, we are concerned with the numerical analysis of a nonlinear implicit difference scheme for Burgers' equation. A priori estimation of the analytical solution is provided in the sense of L ∞-norm when the initial value is bounded in H 1-norm. Conservation, boundedness, and unique solvability are proved at length. Inspired by the method of the priori estimation for the analytical solution, we prove the convergence and stability of the difference scheme in L ∞-norm. Finally, numerical examples are carried out to verify our theoretical results.

No abstract