Generalized Kronecker product splitting iteration for the solution of implicit Runge–Kutta and boundary value methods

This paper is concerned with a generalization of the Kronecker product splitting (KPS) iteration for solving linear systems arising in implicit Runge–Kutta and boundary value methods discretizations of ordinary differential equations. It is shown that the new scheme can outperform the standard KPS method in some situations and can be used as an effective preconditioner for Krylov subspace methods. Numerical experiments are presented to demonstrate the effectiveness of the methods. Copyright © 2014 John Wiley & Sons, Ltd.