A Two-Step Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Special Second Order Oscillatory Differential Equation

被引：0
|
作者：
Ahmad, S. Z. [1 ]
Ismail, F. [1 ,2 ]
Senu, N. [1 ,2 ]
机构：
[1] Univ Putra Malaysia, Dept Math, Serdang 43400, Selangor, Malaysia
[2] Univ Putra Malaysia, Inst Math Res, Serdang 43400, Selangor, Malaysia
来源：
MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES | 2016年 / 10卷
关键词：
Semi-Implicit Hybrid Method; Two-step Methods; Oscillatory problems; Trigonometrically-fitted;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we derived a semi-implicit hybrid method (SIHM) which is a two-step method to solve special second order ordinary differential equations (ODEs). The SIHM which is three-stage and fourth-order is then trigonometrically fitted and denoted by TF-SIHM3(4). The method is constructed using trigonometrically fitted properties instead of using phase-lag and amplification properties. Numerical integration show that TF-SIHM3(4) is more accurate in term of accuracy compared to the existing explicit and implicit methods of the same order.
引用
收藏
页码：145 / U332
页数：15
相关论文
共 50 条
  • [1] Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs
    Franco, J. M.
    Gomez, I.
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 232 : 643 - 657
  • [2] Trigonometrically fitted two-step hybrid methods for special second order ordinary differential equations
    D' Ambrosio, R.
    Ferro, M.
    Paternoster, B.
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2011, 81 (05) : 1068 - 1084
  • [3] A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations
    Ahmad, Sufia Zulfa
    Ismail, Fudziah
    Senu, Norazak
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2016, 2016
  • [4] Symmetric trigonometrically-fitted two-step hybrid methods for oscillatory problems
    Li, Jiyong
    Wang, Xianfen
    Deng, Shuo
    Wang, Bin
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 344 : 115 - 131
  • [5] Trigonometrically Fitted Two Step Hybrid method for the numerical integration of second order IVPs
    Monovasilis, Th.
    Kalogiratou, Z.
    Simos, T. E.
    [J]. PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM-2015), 2016, 1738
  • [6] Revised trigonometrically fitted two-step hybrid methods with equation dependent coefficients for highly oscillatory problems
    Fang, Yonglei
    Yang, Yanping
    You, Xiong
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 318 : 266 - 278
  • [7] Trigonometrically fitted multi-step hybrid methods for oscillatory special second-order initial value problems
    Li, Jiyong
    Lu, Ming
    Qi, Xuli
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (05) : 979 - 997
  • [8] SOLVING OSCILLATORY PROBLEMS USING A BLOCK HYBRID TRIGONOMETRICALLY FITTED METHOD WITH TWO OFF-STEP POINTS
    Ngwane, Fidele F.
    Jator, Samuel N.
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, : 119 - 132
  • [9] An eighth-order exponentially fitted two-step hybrid method of explicit type for solving orbital and oscillatory problems
    J. M. Franco
    L. Rández
    [J]. Numerical Algorithms, 2018, 78 : 243 - 262
  • [10] Solving the Telegraph and Oscillatory Differential Equations by a Block Hybrid Trigonometrically Fitted Algorithm
    Ngwane, F. F.
    Jator, S. N.
    [J]. INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 2015
12345