An extrapolated splitting method for solving semi-discretized parabolic differential equations

Abstract

An extrapolated Peaceman–Rachford–Strang splitting method is designed and examined in application to semi-discretized parabolic partial differential equations. A multi-product expansion method is implemented to improve the order of accuracy beyond second order in time. The numerical analysis of the high-order splitting method is further validated and illustrated through numerical experiments of linear and nonlinear partial differential equations.

Keywords:

• Peaceman–Rachford–Strang splitting
• splitting method
• multi-product expansion
• Sheng–Suzuki barrier

2010 AMS Subject Classifications::

• 65M15
• 65L05
• 65M70
• 65L06

Acknowledgements

The authors would like to acknowledge the referees for the helpful suggestions, for which greatly improved the clarity and readability of this paper.