Stability and convergence of difference schemes for multi-dimensional parabolic equations with variable coefficients and mixed derivatives

ABSTRACT

We present second-order difference schemes for a class of parabolic problems with variable coefficients and mixed derivatives. The solvability, stability and convergence of the schemes are rigorously analysed by the discrete energy method. Using the Richardson extrapolation technique, the fourth-order accurate numerical approximations both in time and space are obtained. It is noted that the Richardson extrapolation algorithms can preserve stability of the original difference scheme. Finally, numerical examples are carried out to verify the theoretical results.

KEYWORDS:

• Parabolic equation
• mixed derivatives
• variable coefficients
• finite difference scheme
• stability
• convergence
• Richardson extrapolation

2010 AMS SUBJECT CLASSIFICATIONS:

• 65M06
• 65M12
• 65M15

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [No. 11671081] and the Scientific Research Foundation of Graduate School of Southeast University [Grant No. YBJJ1716].