A Trigonometrically Adapted Embedded Pair of Explicit Runge-Kutta-Nyström Methods to Solve Periodic Systems

SSRN Electronic Journal ◽

10.2139/ssrn.3924308 ◽

2021 ◽

Author(s):

Musa Ahmed Demba ◽

Higinio Ramos ◽

Poom Kumam ◽

Wiboonsak Watthayu ◽

Norazak Senu ◽

...

Keyword(s):

Periodic Systems ◽

Nyström Methods ◽

Runge Kutta

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Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods

10.1063/1.4897864 ◽

2014 ◽

Cited By ~ 4

Author(s):

Theodore Monovasilis ◽

Zacharoula Kalogiratou ◽

T. E. Simos

Keyword(s):

Nyström Methods ◽

Exponentially Fitted ◽

Runge Kutta

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Explicit parallel two-step Runge-Kutta-Nyström methods

Computers & Mathematics with Applications ◽

10.1016/0898-1221(96)00117-4 ◽

1996 ◽

Vol 32 (3) ◽

pp. 119-130 ◽

Cited By ~ 15

Author(s):

N.h. Cong

Keyword(s):

Nyström Methods ◽

Runge Kutta

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High-order zero-dissipative Runge-Kutta-Nyström methods

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(98)00081-8 ◽

1998 ◽

Vol 95 (1-2) ◽

pp. 157-161 ◽

Cited By ~ 10

Author(s):

Ch. Tsitouras

Keyword(s):

High Order ◽

Order Zero ◽

Nyström Methods ◽

Runge Kutta

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Continuous Runge-Kutta(-Nyström) methods with reduced phase-errors

Journal of Computational and Applied Mathematics ◽

10.1016/0377-0427(95)00027-5 ◽

1996 ◽

Vol 69 (1) ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

G. Papageorgiou ◽

Ch. Tsitouras

Keyword(s):

Nyström Methods ◽

Phase Errors ◽

Runge Kutta

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A 5(3) pair of explicit Runge–Kutta–Nyström methods for oscillatory problems

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2006.07.016 ◽

2007 ◽

Vol 45 (5-6) ◽

pp. 708-716 ◽

Cited By ~ 14

Author(s):

Hans Van de Vyver

Keyword(s):

Nyström Methods ◽

Runge Kutta

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New modified Runge–Kutta–Nyström methods for the numerical integration of the Schrödinger equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2010.06.046 ◽

2010 ◽

Vol 60 (6) ◽

pp. 1639-1647 ◽

Cited By ~ 137

Author(s):

Z. Kalogiratou ◽

Th. Monovasilis ◽

T.E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Integration ◽

Schrodinger Equation ◽

Nyström Methods ◽

Runge Kutta

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Optimal time order when implicit Runge–Kutta–Nyström methods solve linear partial differential equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2007.01.001 ◽

2008 ◽

Vol 58 (5) ◽

pp. 539-562 ◽

Cited By ~ 6

Author(s):

I. Alonso-Mallo ◽

B. Cano ◽

M.J. Moreta

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Optimal Time ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Nyström Methods ◽

Time Order ◽

Runge Kutta

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Two-derivative Runge-Kutta-Nyström methods for second-order ordinary differential equations

Numerical Algorithms ◽

10.1007/s11075-015-9979-4 ◽

2015 ◽

Vol 70 (4) ◽

pp. 897-927 ◽

Cited By ~ 16

Author(s):

Zhaoxia Chen ◽

Zeyu Qiu ◽

Juan Li ◽

Xiong You

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Second Order ◽

Nyström Methods ◽

Runge Kutta

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An alternative approach for order conditions of Runge-Kutta-Nyström methods

Advances in Computational Mathematics ◽

10.1007/s10444-021-09894-3 ◽

2021 ◽

Vol 47 (5) ◽

Author(s):

Xue Sun ◽

Zhongli Liu ◽

Hongjiong Tian

Keyword(s):

Order Conditions ◽

Nyström Methods ◽

Alternative Approach ◽

Runge Kutta

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Runge–Kutta (–Nyström) Methods for Oscillatory Differential Equations

Structure-Preserving Algorithms for Oscillatory Differential Equations ◽

10.1007/978-3-642-35338-3_1 ◽

2013 ◽

pp. 1-25

Author(s):

Xinyuan Wu ◽

Xiong You ◽

Bin Wang

Keyword(s):

Differential Equations ◽

Nyström Methods ◽

Runge Kutta

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