Nested Second Derivative Two-Step Runge–Kutta Methods

被引:0
|
作者
Olatunji P.O. [1 ]
Ikhile M.N.O. [2 ]
Okuonghae R.I. [2 ]
机构
[1] Department of Mathematical Sciences, Adekunle Ajasin University, P.M.B 001, Akungba Akoko, Ondo State
[2] Advanced Research Laboratory, Department of Mathematics, University of Benin, P.M.B 1154, Benin City
关键词
A-; L-; stability; Error estimation; Nested second derivative two-step Runge–Kutta methods; Order reduction; Second derivative general linear methods; Two-step Runge–Kutta methods;
D O I
10.1007/s40819-021-01169-1
中图分类号
学科分类号
摘要
Two-step Runge–Kutta (TSRK) methods are Runge–Kutta methods that depend on stage values at two consecutive steps. Second derivative Two-step Runge–Kutta (SD-TSRK) methods are extension of TSRK methods in which second derivatives as well as first derivatives are computed. General linear methods (GLMs) were introduced as a generalization of Runge–Kutta methods and linear multistep methods, and have also been extended to second derivative general linear methods (SD-GLMs). This paper presents SD-TSRK methods that are nested in their stages and mono-implicit in their output as SD-GLMs; these methods are referred to as nested second derivative two-step Runge–Kutta methods. L-stable members have been developed for the numerical integration of ordinary differential equations and how possible instances of order reduction can be avoided along with other theoretical order analysis are also considered. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.
引用
收藏
相关论文
共 50 条
  • [31] On the implementation of explicit two-step peer methods with Runge-Kutta stability
    Abdi, A.
    Hojjati, G.
    Jackiewicz, Z.
    Podhaisky, H.
    Sharifi, M.
    APPLIED NUMERICAL MATHEMATICS, 2023, 186 : 213 - 227
  • [32] A CLASS OF IMPLICIT-EXPLICIT TWO-STEP RUNGE-KUTTA METHODS
    Zharovsky, Evgeniy
    Sandu, Adrian
    Zhang, Hong
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2015, 53 (01) : 321 - 341
  • [33] Functionally fitted explicit pseudo two-step Runge-Kutta methods
    Hoang, Nguyen S.
    Sidje, Roger B.
    APPLIED NUMERICAL MATHEMATICS, 2009, 59 (01) : 39 - 55
  • [34] Two-step Runge–Kutta methods for Volterra integro-differential equations
    Wen J.
    Huang C.
    Guan H.
    International Journal of Computer Mathematics, 2024, 101 (01) : 37 - 55
  • [35] Two-step Runge-Kutta: Theory and practice
    Tracogna, S
    Welfert, B
    BIT, 2000, 40 (04): : 775 - 799
  • [36] Two-Step Runge-Kutta: Theory and Practice
    S. Tracogna
    B. Welfert
    BIT Numerical Mathematics, 2000, 40 : 775 - 799
  • [37] Parallel-iterated pseudo two-step Runge–Kutta methods with step size control
    Nguyen Huu Cong
    Nguyen Thu Thuy
    Japan Journal of Industrial and Applied Mathematics, 2014, 31 : 441 - 460
  • [38] Comparison of Two Derivative Runge Kutta Methods.
    Monovasilis, Th.
    Kalogiratou, Z.
    Simos, T. E.
    INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2018 (ICCMSE-2018), 2018, 2040
  • [39] Two-step high order starting values for implicit Runge-Kutta methods
    Calvo, M
    Laburta, MP
    Montijano, JI
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2003, 19 (04) : 401 - 412
  • [40] Explicit two-step Runge-Kutta methods for computational fluid dynamics solvers
    Figueroa, Alejandro
    Jackiewicz, Zdzislaw
    Lohner, Rainald
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2021, 93 (02) : 429 - 444