A four-stage implicit Runge-Kutta-Nyström method with variable coefficients for solving periodic initial value problems

Kazufumi Ozawa

doi:10.1007/bf03167523

A four-stage implicit Runge-Kutta-Nyström method with variable coefficients for solving periodic initial value problems

Japan Journal of Industrial and Applied Mathematics ◽

10.1007/bf03167523 ◽

1999 ◽

Vol 16 (1) ◽

pp. 25-46 ◽

Cited By ~ 17

Author(s):

Kazufumi Ozawa

Keyword(s):

Initial Value Problems ◽

Variable Coefficients ◽

Initial Value ◽

Nyström Method ◽

Nystrom Method ◽

Periodic Initial Value Problems ◽

Runge Kutta

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An embedded 4(3) pair of explicit trigonometrically-fitted Runge-Kutta-Nystrom method for solving periodic initial value problems

Applied Mathematical Sciences ◽

10.12988/ams.2017.7262 ◽

2017 ◽

Vol 11 ◽

pp. 819-838 ◽

Cited By ~ 1

Author(s):

M. A. Demba ◽

N. Senu ◽

F. Ismail

Keyword(s):

Initial Value Problems ◽

Initial Value ◽

Nyström Method ◽

Nystrom Method ◽

Periodic Initial Value Problems ◽

Runge Kutta

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A Runge—Kutta—Nyström method for the numerical integration of special second-order periodic initial-value problems

Journal of Computational and Applied Mathematics ◽

10.1016/0377-0427(92)00114-o ◽

1994 ◽

Vol 51 (3) ◽

pp. 317-326 ◽

Cited By ~ 34

Author(s):

T.E. Simos ◽

E. Dimas ◽

A.B. Sideridis

Keyword(s):

Numerical Integration ◽

Initial Value Problems ◽

Second Order ◽

Initial Value ◽

Nyström Method ◽

Nystrom Method ◽

Periodic Initial Value Problems ◽

Runge Kutta

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Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions

Applied Mathematics Letters ◽

10.1016/s0893-9659(01)00121-5 ◽

2002 ◽

Vol 15 (2) ◽

pp. 217-225 ◽

Cited By ~ 96

Author(s):

T.E. Simos

Keyword(s):

Numerical Solution ◽

Initial Value Problems ◽

Initial Value ◽

Nyström Method ◽

Nystrom Method ◽

Oscillating Solutions ◽

Exponentially Fitted ◽

Runge Kutta

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An optimized explicit Runge–Kutta–Nyström method for the numerical solution of orbital and related periodical initial value problems

Computer Physics Communications ◽

10.1016/j.cpc.2011.11.002 ◽

2012 ◽

Vol 183 (3) ◽

pp. 470-479 ◽

Cited By ~ 29

Author(s):

A.A. Kosti ◽

Z.A. Anastassi ◽

T.E. Simos

Keyword(s):

Numerical Solution ◽

Initial Value Problems ◽

Initial Value ◽

Nyström Method ◽

Nystrom Method ◽

Runge Kutta

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Construction of an optimized explicit Runge–Kutta–Nyström method for the numerical solution of oscillatory initial value problems

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2011.04.046 ◽

2011 ◽

Vol 61 (11) ◽

pp. 3381-3390 ◽

Cited By ~ 131

Author(s):

A.A. Kosti ◽

Z.A. Anastassi ◽

T.E. Simos

Keyword(s):

Numerical Solution ◽

Initial Value Problems ◽

Initial Value ◽

Nyström Method ◽

Nystrom Method ◽

Oscillatory Initial Value Problems ◽

Runge Kutta

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A phase-fitted Runge–Kutta–Nyström method for the numerical solution of initial value problems with oscillating solutions

Computer Physics Communications ◽

10.1016/j.cpc.2009.05.014 ◽

2009 ◽

Vol 180 (10) ◽

pp. 1839-1846 ◽

Cited By ~ 29

Author(s):

D.F. Papadopoulos ◽

Z.A. Anastassi ◽

T.E. Simos

Keyword(s):

Numerical Solution ◽

Initial Value Problems ◽

Initial Value ◽

Nyström Method ◽

Nystrom Method ◽

Oscillating Solutions ◽

Runge Kutta

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Block Runge-Kutta methods for periodic initial-value problems

Computers & Mathematics with Applications ◽

10.1016/0898-1221(95)00183-y ◽

1996 ◽

Vol 31 (1) ◽

pp. 69-83 ◽

Cited By ~ 23

Author(s):

G. Avdelas ◽

T.E. Simos

Keyword(s):

Initial Value Problems ◽

Initial Value ◽

Periodic Initial Value Problems ◽

Runge Kutta

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A fifth order phase-fitted Runge-Kutta-Nyström method for periodic initial value problems

10.1063/1.4823909 ◽

2013 ◽

Author(s):

M. Mohamad ◽

N. Senu ◽

M. Suleiman ◽

F. Ismail

Keyword(s):

Initial Value Problems ◽

Initial Value ◽

Periodic Initial Value Problems ◽

Runge Kutta ◽

Fifth Order

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A low-order embedded Runge—Kutta method for periodic initial-value problems

Journal of Computational and Applied Mathematics ◽

10.1016/0377-0427(92)90013-n ◽

1992 ◽

Vol 44 (2) ◽

pp. 235-244 ◽

Cited By ~ 26

Author(s):

A.B. Sideridis ◽

T.E. Simos

Keyword(s):

Initial Value Problems ◽

Kutta Method ◽

Initial Value ◽

Runge Kutta Method ◽

Periodic Initial Value Problems ◽

Runge Kutta ◽

Low Order

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A functional fitting Runge-Kutta-Nyström method with variable coefficients

Japan Journal of Industrial and Applied Mathematics ◽

10.1007/bf03167448 ◽

2002 ◽

Vol 19 (1) ◽

pp. 55-85 ◽

Cited By ~ 10

Author(s):

Kazufumi Ozawa

Keyword(s):

Variable Coefficients ◽

Nyström Method ◽

Nystrom Method ◽

Functional Fitting ◽

Runge Kutta

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