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

Authors:
Ch. Tsitouras
Affiliations:
Faculty of Applied Sciences, Mathematics Department, National Technical University, Zografou Campus, GR15780 Athens, Greece
Venue:
Applied Mathematics and Computation
Year:
2003

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Abstract

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.