An efficient and computational effective method for second order problems

被引：49
|
作者：
Ma, Jing [1 ]
Simos, T. E. [2 ,3 ]
机构：
[1] Changan Univ, Sch Informat Engn, Xian 710064, Shaanxi, Peoples R China
[2] Univ Peloponnese, Fac Econ Management & Informat, Dept Informat & Telecommun, Lab Computat Sci, Tripoli 22100, Greece
[3] 10 Konitsis St, Athens 17564, Greece
来源：
JOURNAL OF MATHEMATICAL CHEMISTRY | 2017年 / 55卷 / 08期
关键词：
Phase-lag; Derivative of the phase-lag; Initial value problems; Oscillating solution; Symmetric; Hybrid; Multistep; Schrodinger equation; VANISHED PHASE-LAG; INITIAL-VALUE-PROBLEMS; RADIAL SCHRODINGER-EQUATION; PREDICTOR-CORRECTOR METHOD; SYMMETRIC 2-STEP METHOD; EXPLICIT 4-STEP METHOD; P-STABLE METHOD; TRIGONOMETRICALLY-FITTED FORMULAS; KUTTA-NYSTROM METHODS; NUMERICAL-SOLUTION;
D O I：
10.1007/s10910-017-0753-9
中图分类号：
O6 [化学];
学科分类号：
0703 ;
摘要：
An efficient and computational effective algorithm is introduced, for the first time in the literature, in the present paper. The main properties of the scheme are: (1) the algorithm is a two-step scheme, (2) the algorithm is symmetric one, (3) it is a hight algebraic order scheme (i.e of eight algebraic order), (4) it is a three-stages algorithm, (5) the first layer of the new method is based on an approximation to the point , (6) the scheme has vanished phase-lag and its first, second and third derivatives, (7) the new proposed algorithm has an interval of periodicity equal to . For the present new scheme we study: (1) its construction, (2) its error analysis (3) its stability analysis. Finally, the investigation of the effectiveness of the new algorithm leads to its application to systems of differential equations arising from the Schrodinger equation.
引用
收藏
页码：1649 / 1668
页数：20
相关论文
共 50 条
  • [1] An efficient and computational effective method for second order problems
    Jing Ma
    T. E. Simos
    Journal of Mathematical Chemistry, 2017, 55 : 1649 - 1668
  • [2] An efficient computational method for second order boundary value problems of nonlinear differential equations
    Zhou, Yongfang
    Lin, Yinzhen
    Cui, Minggen
    APPLIED MATHEMATICS AND COMPUTATION, 2007, 194 (02) : 354 - 365
  • [3] An Efficient Method for Solving Second-Order Fuzzy Order Fuzzy Initial Value Problems
    Dallashi, Qamar
    Syam, Muhammed I.
    SYMMETRY-BASEL, 2022, 14 (06):
  • [4] An efficient method for second order boundary value problems with two point boundary conditions
    Nemani, SS
    Garey, LE
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2002, 79 (09) : 1001 - 1008
  • [5] An efficient computational method for stress concentration problems
    Shrestha, S
    Ohga, M
    STRUCTURAL ENGINEERING AND MECHANICS, 2006, 22 (05) : 613 - 629
  • [6] An adaptive time stepping method with efficient error control for second-order evolution problems
    JianGuo Huang
    JunJiang Lai
    Tao Tang
    Science China Mathematics, 2013, 56 : 2753 - 2771
  • [7] An adaptive time stepping method with efficient error control for second-order evolution problems
    Huang JianGuo
    Lai JunJiang
    Tang Tao
    SCIENCE CHINA-MATHEMATICS, 2013, 56 (12) : 2753 - 2771
  • [8] Efficient iterations for Gauss methods on second-order problems
    González-Pinto, S
    Pérez-Rodríguez, S
    Rojas-Bello, R
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 189 (1-2) : 80 - 97
  • [9] On a Method of Studying Identification Problems for Second Order Equations
    Anikonov Y.E.
    Neshchadim M.V.
    Journal of Applied and Industrial Mathematics, 2019, 13 (01) : 11 - 21
  • [10] Efficient computational method for matrix function in dynamic problems
    Wu, Feng
    Zhu, Li
    Zhao, Yuelin
    Zhang, Kailing
    Yan, Jun
    Zhong, Wanxie
    Shi, Qinghua
    ACTA MECHANICA SINICA, 2023, 39 (08)
12345