On two linearized difference schemes for Burgers’ equation

Burgers’ equation can model several physical phenomena. In the first part of this work, we derive a three-level linearized difference scheme for Burgers’ equation, which is then proved to be energy conservative, unique solvable and unconditionally convergent in the maximum norm by the energy method combining with the inductive method. In the second part of the work, we prove the L∞ unconditional convergence of a two-level linearized difference scheme for Burgers’ equation proposed by Sheng [A new difference scheme for Burgers equation, J. Jiangsu Normal Univ. 30 (2012), pp. 39–43], which was proved previously conditionally convergent.