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

Coleman, 2003, Order conditions for a class of two-step methods for y″=f(x,y), IMA J. Numer. Anal., 23, 197, 10.1093/imanum/23.2.197

Coleman, 1996, P-stability and exponential-fitting methods for y″=f(x,y), IMA J. Numer. Anal., 16, 179, 10.1093/imanum/16.2.179

Franco, 2004, Runge–Kutta methods adapted to the numerical integration of oscillatory problems, Appl. Numer. Math., 50, 427, 10.1016/j.apnum.2004.01.005

Franco, 2006, A class of explicit two-step hybrid methods for second-order IVPs, J. Comput. Appl. Math., 187, 41, 10.1016/j.cam.2005.03.035

Lambert, 1976, Symmetric multistep methods for periodic initial value problems, J. Inst. Math. Appl., 18, 189, 10.1093/imamat/18.2.189

Paternoster, 1998, Runge–Kutta(–Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials, Appl. Numer. Math., 28, 401, 10.1016/S0168-9274(98)00056-7

Van de Vyver, 2005, Stability and phase-lag analysis of explicit Runge–Kutta methods with variable coefficients for oscillatory problems, Comput. Phys. Comm., 173, 115, 10.1016/j.cpc.2005.07.007

van der Houwen, 1987, Explicit Runge–Kutta(–Nyström) methods with reduced phase errors for computing oscillating solution, SIAM J. Numer. Anal., 24, 595, 10.1137/0724041

Vanden Berghe, 1999, Exponentially fitted Runge–Kutta methods, Comput. Phys. Comm., 123, 7, 10.1016/S0010-4655(99)00365-3

Vanden Berghe, 2000, Exponentially fitted explicit Runge–Kutta methods, J. Comput. Appl. Math., 125, 107, 10.1016/S0377-0427(00)00462-3