High algebraic, high phase-lag order embedded Numerov-type methods for oscillatory problems

摘要

An embedded Numerov-type method of algebraic order eight with phase-lag orders 10–20 for the numerical integration of second-order periodic initial-value problems is developed in this paper.The method has 10 stages. An error estimation, based on varying the phase-lag order, is introduced and an embedded technique is described. Each method of the embedded pair has a large interval of periodicity. Theoretical evidence and numerical and theoretical results obtained for several well-known problems show the efficiency of the new methods.