Runge–Kutta methods of dynamic iteration for index-2 differential–algebraic equations

Abstract

This paper investigates a few forms of Runge–Kutta methods based on dynamic iteration for index-2 differential–algebraic equations. In particular, the convergence of iterative Runge–Kutta methods is proven for the complex systems. The iterative processes allow implementation with different meshes, which can help improve the accuracy and the stability properties of the proposed method. Finally, the iterative schemes how to appropriately implement on the parallel computers are also involved.