Stabilization theory of iterative operator-splitting methods

Abstract

In this paper we present a stabilization theory of iterative operator-splitting methods for linear and nonlinear differential equations. Continuous formulation is described and also the stability for linear and nonlinear cases. We apply linearization techniques to adduce proof of the linear theory. Iterative methods are applied to linearize and couple operator equations. A general theory is derived for linear and nonlinear iterative-splitting methods. Test examples verify the underlying theoretical results.

Keywords:

• operator-splitting method
• iterative-solver method
• stability analysis
• weighting method
• Newton's methods

AMS Subject Classification :

• 80A20
• 80M25
• 74S10
• 76R50
• 35J60
• 35J65
• 65M99
• 65Z05
• 65N12