Weighted sequential splittings and their analysis

Operator splitting is a widely used procedure in the numerical solution of parabolicproblems. Several splitting methods have been constructed and used in the fields of applied mathematics. In this paper the weighted sequential splittings are introduced and their local splitting error is analyzed. New results are presented for the case where the subproblems of the weighted splitting schemes are solved numerically. The results are illustrated with test examples for ordinary differential systems.