The convergence of a new symmetric iterative splitting method for non-autonomous systems

Abstract

The iterative splitting methods have been extensively applied to solve complicated systems of differential equations. In this process, we split the complex problem into several sub-problems, each of which can be solved sequentially. In this paper, we construct a new symmetric iterative splitting scheme based on the Magnus expansion for solving non-autonomous problems. We also study its convergence properties by using the concepts of stability, consistency, and order. Several numerical examples are illustrated to confirm the theoretical results by comparing frequently used methods.

Keywords:

• iterative scheme
• non-autonomous system
• convergence analysis
• Magnus series

Keywords:

• 2010 AMS Subject Classifications:
• 65L20
• 65L70
• 65M12