A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions

作者：Fang Yonglei; Wu Xinyuan^*

来源：Applied Numerical Mathematics, 2008, 58(3): 341-351.

DOI：10.1016/j.apnum.2006.12.003

• trigonometrical fitting
• Numerov-type method
• oscillating solution
• second-order IVPs

A new kind of trigonometrically fitted explicit Numerov-type method for the numerical integration of second-order initial value problems (IVPs) with oscillating or periodic solutions is presented in this paper. This new method is based on the original fifth-order method which is dispersion of order eight and dissipation of order five proposed in [J.M. Franco, A class of explicit two-step hybrid methods for second-order IVPs, J. Comput. Appl. Math. 187 (2006) 41-57]. Using trigonometrically filling, we derive a more efficient method with higher accuracy for the numerical integration of second-order IVPs with oscillating solutions, and we analyze the stability, phase-lag(dispersion) and dissipation by the theory considered by Coleman and Ixaru (see I.J.P. Coleman, L.Gr. Ixaru, P-stability and exponential-fitting methods for y '' = f (x, y), IMA J. Numer. Anal. 16 (1996) 179-199 1). Numerical experiments are carried out to show the efficiency of our new method in comparison with the methods proposed in [J.M. Franco, A class of explicit two-step hybrid methods for second-order IVPs, J. Comput. Appl. Math. 187 (2006) 41-571 and the exponentially fitted fourth order RKN method derived in [J.M. Franco, Exponentially fitted explicit Runge-Kutta-Nystrom methods, J. Cornput. Appl. Math. 167 (2004) 1-19].

• 出版日期2008-3
• 单位南京大学