Locally one-dimensional-alternating segment explicit–implicit and locally one-dimensional-alternating segment Crank–Nicolson methods for two-dimension parabolic equations

Abstract

In the paper two new locally one-dimensional alternating segment schemes for solving the 2-D parabolic problems are developed. The parabolic problems can be solved efficiently over decomposed sub-domains. Two schemes are proved to be unconditionally stable and numerical experiments show the validity of the schemes.

Keywords:

• locally one-dimension
• alternating segment scheme
• domain decomposition
• parabolic problem
• parallel algorithm

2000 AMS Subject Classifications:

• 65M06
• 65M12
• 65Y05

Acknowledgements

S.H. Zhang was supported by Shandong Provincial Education Department, P.R.China for her visit to York University, and was supported by Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province (BS2013NJ016) and the Project-sponsored by SRF for ROCS, SEM. D. Liang was supported by Natural Sciences and Engineering Research Council of Canada, and was supported partly by the National Natural Science Foundation of China under grant 11271232.