ASYMPTOTIC FACTORIZATION OF OPERATORS IN COMPLEX TIME

Operator splitting with complex fractional-steps, perhaps regarded as a mathematical curiosity, is shown to be a feasible tool for stable numerical solution of ordinary as well as partial differential equations. This result may appear surprising, as in Q. Sheng stability of a splitting is defined as equivalent to the presence of all-positive fractional steps. Equivalences between the classes of fractional-step operator splittings for autonomous nonlinear scalar differential equations and splittings for vector evolution equations which involve linear operators are established. The implication is that results for the well-investigated linear case can be applied over a larger class of problems. Further analysis reveals circumstances in which the splitting concept can be used to broaden the range of stability of algorithms which may be used for the numerical solution of ordinary differential equations. Thus, alternatives to the usual methods for stiff systems integration become available. © 1991.