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 H¹‐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.

中文翻译：

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Burgers方程的保守差分格式的逐点估计

在本文中，我们关注Burgers方程的非线性隐式差分格式的数值分析。解析解的先验估计中的意义上提供大号^∞范数时的初始值在为界ħ ¹范数。证明了保守性，有界性和独特的可溶性。通过用于分析溶液中的先验估计的方法的启发，我们证明在差分方案的收敛性和稳定性大号^∞范数。最后，通过数值算例验证了我们的理论结果。