Families of explicit two-step methods for integration of problems with oscillating solutions

We study a new sixth algebraic order, explicit Numerov-type family of methods. Using every free parameter of the family, even its nodes, we manage to derive two methods. The first with phase-lag of order 12, while the other method has one stage less. This is a considerable improvement over the 10th order phase-lag order methods found in the literature until now. Numerical experiments confirm the superiority of our new methods over older methods. (C) 2002 Elsevier Science Inc. All rights reserved.