A new family of 7 stages, eighth-order explicit Numerov-type methods

作者：Simos, T. E.^*; Tsitouras, Ch.

来源：Mathematical Methods in the Applied Sciences, 2017, 40(18): 7867-7878.

DOI：10.1002/mma.4570

• constant coefficients
• hybrid Numerov methods
• initial value problem
• interval of periodicity
• numerical solution
• phase-lag

In this paper, we consider the integration of the special second-order initial value problem. Hybrid Numerov methods are used, which are constructed in the sense of Runge-Kutta ones. Thus, the Taylor expansions at the internal points are matched properly in the final expression. A new family of such methods attaining eighth algebraic order is given at a cost of only 7 function evaluations per step. The new family provides us with an extra parameter, which is used to increase phase-lag order to 18. We proceed with numerical tests over a standard set of problems for these cases. Appendices implementing the symbolic construction of the methods and derivation of their coefficients are also given.

• 出版日期2017-12
• 单位内江师范学院