A 4(3) Pair Runge-Kutta-Nystrom Method for Periodic Initial Value Problems

被引：0
|
作者：
Senu, Norazak [1 ]
Suleiman, Mohamed [1 ]
Ismail, Fudziah [1 ]
Othman, Mohamed [2 ]
机构：
[1] Univ Putra Malaysia, Fak Sains, Jabatan Matemat, Upm Serdang 43400, Selangor, Malaysia
[2] Univ Putra Malaysia, Fak Sains Komputer Dan Teknol Maklumat, Jabatan Teknol Komunikasi Dan Rangkaian, Upm Serdang 43400, Selangor, Malaysia
来源：
SAINS MALAYSIANA | 2010年 / 39卷 / 04期
关键词：
Oscillatory solutions; Phase-lag; Runge-Kutta-Nystrom methods; NUMERICAL-INTEGRATION; OSCILLATING SOLUTIONS;
D O I：
暂无
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
A new embedded 4(3) pair explicit four-stage fourth-order Runge-Kutta-Nystrom (RKN) method was developed to integrate second-order differential equations of the form y '' = f (x, y) where the solution was oscillatory. Presented is a method which has high order dispersion with a 'small' principal local truncation error coefficient. The stability analysis of the method derived is also given. Numerical comparisons of this new method with RK4(3) and RKN4(3) D methods show its clear advantage in terms of function evaluations and computation time.
引用
收藏
页码：639 / 646
页数：8
相关论文
共 50 条
  • [31] A PAIR OF RUNGE-KUTTA-NYSTROM FORMULAS FOR Y''=F(X,Y)
    FEHLBERG, E
    FILIPPI, S
    GRAF, J
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1986, 66 (07): : 265 - 270
  • [32] Embedded Exponentially-Fitted Explicit Runge-Kutta-Nystrom Methods for Solving Periodic Problems
    Demba, Musa Ahmed
    Kumam, Poom
    Watthayu, Wiboonsak
    Phairatchatniyom, Pawicha
    COMPUTATION, 2020, 8 (02)
  • [33] An Optimized Runge-Kutta-Nystrom Method for the Numerical Solution of the Schrodinger Equation and Related Problems
    Papadopoulos, D. F.
    Anastassi, Z. A.
    Simos, T. E.
    MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2010, 64 (02) : 551 - 566
  • [34] A Fourth Order Phase-Fitted Runge-Kutta-Nystrom Method for Oscillatory Problems
    Wing, Moo Kwong
    Senu, Norazak
    Ismail, Fudziah
    Suleiman, Mohamed
    PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM20): RESEARCH IN MATHEMATICAL SCIENCES: A CATALYST FOR CREATIVITY AND INNOVATION, PTS A AND B, 2013, 1522 : 316 - 322
  • [35] A functional fitting Runge-Kutta-Nystrom method with variable coefficients
    Ozawa, K
    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2002, 19 (01) : 55 - 85
  • [36] Embedded exponentially fitted Runge-Kutta-Nystrom method for the numerical solution of orbital problems
    Van de Vyver, Hans
    NEW ASTRONOMY, 2006, 11 (08) : 577 - 587
  • [37] A trigonometrically adapted 6(4) explicit Runge-Kutta-Nystrom pair to solve oscillating systems
    Demba, Musa Ahmed
    Ramos, Higinio
    Kumam, Poom
    Watthayu, Wiboonsak
    Senu, Norazak
    Ahmed, Idris
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (01) : 560 - 578
  • [38] Functionally fitted Runge-Kutta-Nystrom methods
    Hoang, N. S.
    Sidje, R. B.
    BIT NUMERICAL MATHEMATICS, 2016, 56 (01) : 129 - 150
  • [39] Functional continuous Runge-Kutta-Nystrom methods
    Eremin, Alexey S.
    ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2016,
  • [40] Embedded pair of extended Runge-Kutta-Nystrom type methods for perturbed oscillators
    Fang, Yonglei
    Ming, Qinghe
    APPLIED MATHEMATICAL MODELLING, 2010, 34 (09) : 2665 - 2675
12345