On two linearized difference schemes for Burgers’ equation

Abstract

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.

Keywords:

• Burgers’ equation
• finite-difference scheme
• convergence
• solvability
• L_∞-norm

2010 AMS Subject Classifications:

• 65M06
• 65M12
• 65M15

Acknowledgements

The research is supported by National Natural Science Foundation of China (No.11271068).