Modified two-derivative Runge–Kutta methods for the Schrödinger equation

被引：0
|
作者：
Yanping Yang
Yonglei Fang
Xiong You
机构：
[1] Zaozhuang University,School of Mathematics and Statistics
[2] Nanjing Agricultural University,Department of Applied Mathematics
来源：
Journal of Mathematical Chemistry | 2018年 / 56卷
关键词：
Two-derivative Runge–Kutta method; Schrödinger equation; Phase-lag; Error analysis;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A family of modified two-derivative Runge–Kutta (MTDRK) methods for the integration of the Schrödinger equation are obtained. Two new three-stage and fifth order TDRK methods are derived. The numerical results in the integration of the radial Schrödinger equation with the Woods–Saxon potential are reported to show the high efficiency of our new methods. The results of the error analysis are illustrated by the resonance problem.
引用
收藏
页码：799 / 812
页数：13
相关论文
共 50 条
  • [41] Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation
    Senu, N.
    Lee, K. C.
    Ahmadian, A.
    Ibrahim, S. N. I.
    ALEXANDRIA ENGINEERING JOURNAL, 2022, 61 (08) : 5819 - 5835
  • [42] New two-derivative implicit-explicit Runge-Kutta methods for stiff reaction-diffusion systems
    Singh, Ankit
    Maurya, Vikas
    Rajpoot, Manoj K.
    JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 471
  • [43] Trigonometrically fitted two-derivative Runge-Kutta-Nystrom methods for second-order oscillatory differential equations
    Chen, Zhaoxia
    Shi, Lei
    Liu, Siyao
    You, Xiong
    APPLIED NUMERICAL MATHEMATICS, 2019, 142 : 171 - 189
  • [44] A Family of Exponentially-fitted Runge–Kutta Methods with Exponential Order Up to Three for the Numerical Solution of the Schrödinger Equation
    Z. A. Anastassi
    T. E. Simos
    Journal of Mathematical Chemistry, 2007, 41 : 79 - 100
  • [45] Two Derivative Runge-Kutta Methods of Order Six
    Kalogiratou, Z.
    Monovasilis, Th
    Simos, T. E.
    INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM-2018), 2019, 2116
  • [46] Construction of Two Derivative Runge Kutta Methods of Order Five
    Kalogiratou, Z.
    Monovasilis, Th.
    Simos, T. E.
    PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2016 (ICNAAM-2016), 2017, 1863
  • [47] Trigonometrical Fitting Conditions for Two Derivative Runge Kutta Methods
    Monovasilis, Th.
    Kalogiratou, Z.
    Simos, T. E.
    PROCEEDINGS OF THE INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2016 (ICCMSE-2016), 2016, 1790
  • [48] The stability of modified Runge-Kutta methods for the pantograph equation
    Liu, M. Z.
    Yang, Z. W.
    Xu, Y.
    MATHEMATICS OF COMPUTATION, 2006, 75 (255) : 1201 - 1215
  • [49] Solution of Schrödinger equation and optical susceptibility for core–shell nanoparticles using Runge–Kutta method
    Abbas Koushki
    Ehsan Koushki
    Abdollah Gholizadeh
    Optical and Quantum Electronics, 2016, 48
  • [50] A family of Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the Schrödinger equation and related problems
    Z. A. Anastassi
    D. S. Vlachos
    T. E. Simos
    Journal of Mathematical Chemistry, 2009, 46
12345