Numerical schemes for the forward–backward heat equation

Abstract

This paper is concerned with a class of forward–backward heat equations. We use Saulyev's scheme to formulate certain approximation schemes. Then a non-overlap domain decomposition method is presented for the numerical solution. The numerical experiments show that the given algorithm is feasible and effective.

Keywords:

• forward–backward heat equation
• Saulyev's scheme
• domain decomposition

2000 AMS Subject Classification :

• 65N22
• 65M06
• 35K05
• 65N55

Acknowledgements

During the preparation of this paper, we have benefited from the help and advice of Pro Cheng. Many thanks to him for discussions, careful reading and helpful comments.