Some Linear Algebra Issues Concerning the Implementation of Blended Implicit Methods

ABSTRACT. In this paper we discuss some linear algebra issues concerning the implementation of blended implicit methods (J. Comput. Appl. Math. 2000; 116:41–62, Appl. Numer. Math. 2002; 42:29–45, J. Comput. Appl. Math. 2004; 164–165:145–158, In Recent Trends in Numerical Analysis, Trigiante D (ed.), Nova Science Publication Inc.: New York, 2001; 81–105) for the numerical solution of ODEs. In particular, we describe the strategies, used in the numerical code BiM (J. Comput. Appl. Math. 2004; 164–165:145–158), for deciding whether re-evaluating the Jacobian and=or the factorization involved in the non-linear splitting for solving the discrete problem.