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 ◽

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Further reduction in the number of independent order conditions for symplectic, explicit Partitioned Runge-Kutta and Runge-Kutta-Nyström methods

Applied Numerical Mathematics ◽

10.1016/0168-9274(95)00047-x ◽

1995 ◽

Vol 18 (1-3) ◽

pp. 107-114 ◽

Author(s):

M.P. Calvo ◽

E. Hairer

Keyword(s):

Order Conditions ◽

Nyström Methods ◽

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Order conditions for canonical Runge-Kutta-Nyström methods

BIT Numerical Mathematics ◽

10.1007/bf01995113 ◽

1992 ◽

Vol 32 (1) ◽

pp. 131-142 ◽

Author(s):

M. P. Calvo ◽

J. M. Sanz-Serna

Keyword(s):

Order Conditions ◽

Nyström Methods ◽

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

10.1063/1.4897864 ◽

2014 ◽

Author(s):

Theodore Monovasilis ◽

Zacharoula Kalogiratou ◽

T. E. Simos

Keyword(s):

Nyström Methods ◽

Exponentially Fitted ◽

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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 ◽

Author(s):

N.h. Cong

Keyword(s):

Nyström Methods ◽

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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 ◽

Author(s):

Ch. Tsitouras

Keyword(s):

Nyström Methods ◽

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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 ◽

Author(s):

G. Papageorgiou ◽

Ch. Tsitouras

Keyword(s):

Nyström Methods ◽

Phase Errors ◽

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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 ◽

Author(s):

Hans Van de Vyver

Keyword(s):

Nyström Methods ◽

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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 ◽

Author(s):

Z. Kalogiratou ◽

Th. Monovasilis ◽

T.E. Simos

Keyword(s):

Schrödinger Equation ◽

Numerical Integration ◽

Schrodinger Equation ◽

Nyström Methods ◽

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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 ◽

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 ◽

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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 ◽

Author(s):

Zhaoxia Chen ◽

Zeyu Qiu ◽

Juan Li ◽

Xiong You

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Second Order ◽

Nyström Methods ◽

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