TY - JOUR AU - Wang, Yong AU - Sun, Min AU - Sun, Hongchun PY - 2016 TI - An optimized explicit TDRK method for solving oscillatory problems JO - Journal of Mathematics and Computer Science SP - 205-210 VL - 16 IS - 2 AB - In this paper, a new optimized explicit two-derivative Runge-Kutta (TDRK) method with frequencydepending coeficients is proposed, which is derived by nullifying the dispersion, the dissipation, and the first derivative of the dispersion. The new method has algebraic order four and is dispersive of order five and dissipative of order four. In addition, the phase analysis of the new method is also presented. Numerical experiments are reported to show the efficiency of the new method. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.016.02.08 DO - 10.22436/jmcs.016.02.08 ID - Wang2016 ER - TY - JOUR TI - An optimized Runge-Kutta method for the solution of orbital problems AU - Z. A. Anastassi AU - T. E. Simos JO - J. Comput. Appl. Math. PY - 2005 DA - 2005// VL - 175 ID - Anastassi2005 ER - TY - JOUR TI - On explicit two-derivative Runge-Kutta methods AU - R. P. K. Chan AU - A. Y. J. Tasi JO - Numer. Algorithms PY - 2010 DA - 2010// VL - 53 ID - Chan2010 ER - TY - JOUR TI - New optimized two-derivative Runge-Kutta type methods for solving the radial Schrödinger equation AU - Y. Fang AU - X. You JO - J. Math. Chem. PY - 2014 DA - 2014// VL - 52 ID - Fang2014 ER - TY - JOUR TI - An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions AU - T. E. Simos JO - Comput. Phys. Comm. PY - 1998 DA - 1998// VL - 115 ID - Simos1998 ER - TY - JOUR TI - Exponentially and trigonometrically fitted methods for the solution of the Schrödinger equation AU - T. E. Simos JO - Acta Appl. Math. PY - 2010 DA - 2010// VL - 110 ID - Simos2010 ER - TY - JOUR TI - A two-step method with vanished phase-lag and its first two derivatives for the numerical solution of the Schrödinger equation AU - T. E. Simos JO - J. Math. Chem. PY - 2011 DA - 2011// VL - 49 ID - Simos2011 ER - TY - JOUR TI - A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation AU - T. E. Simos AU - J. V. Aguiar JO - J. Math. Chem. PY - 2001 DA - 2001// VL - 30 ID - Simos2001 ER - TY - JOUR TI - Exponentially fitted TDRK pairs for the Schrödinger equation AU - Y. Yang AU - K. Wu AU - Y. Fang JO - J. Math. Chem. PY - 2015 DA - 2015// VL - 53 ID - Yang2015 ER - TY - JOUR TI - A new trigonometrically fitted two-derivative Runge-Kutta method for the numerical solution of the Schrödinger equation and related problems AU - Y. Zhang AU - H. Che AU - Y. Fang AU - X. You JO - J. Appl. Math. PY - 2013 DA - 2013 // VL - 2013 ID - Zhang2013 ER -