A FOUR-STAGE THIRD-ORDER SYMPLECTIC EXPLICIT TRIGONOMETRICALLY-FITTED RUNGE--KUTTA--NYSTR\"{O}M METHOD FOR THE NUMERICAL INTEGRATION OF OSCILLATORY INITIAL-VALUE PROBLEMS

M.A. Demba; N. Senu; F. Ismail

doi:10.12732/ijpam.v111i2.3

A FOUR-STAGE THIRD-ORDER SYMPLECTIC EXPLICIT TRIGONOMETRICALLY-FITTED RUNGE--KUTTA--NYSTR\"{O}M METHOD FOR THE NUMERICAL INTEGRATION OF OSCILLATORY INITIAL-VALUE PROBLEMS

International Journal of Pure and Apllied Mathematics ◽

10.12732/ijpam.v111i2.3 ◽

2016 ◽

Vol 111 (2) ◽

Author(s):

M.A. Demba ◽

N. Senu ◽

F. Ismail

Keyword(s):

Numerical Integration ◽

Initial Value Problems ◽

Initial Value ◽

Third Order ◽

Oscillatory Initial Value Problems ◽

Runge Kutta

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Trigonometrically fitted multi-step Runge-Kutta methods for solving oscillatory initial value problems

Numerical Algorithms ◽

10.1007/s11075-016-0252-2 ◽

2017 ◽

Vol 76 (1) ◽

pp. 237-258

Author(s):

Jiyong Li

Keyword(s):

Initial Value Problems ◽

Initial Value ◽

Oscillatory Initial Value Problems ◽

Runge Kutta

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Block Runge-Kutta methods for the numerical integration of initial value problems in ordinary differential equations. II. The stiff case

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10.1090/s0025-5718-1983-0679440-x ◽

1983 ◽

Vol 40 (161) ◽

pp. 193-193

Author(s):

J. R. Cash

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Numerical Integration ◽

Initial Value Problems ◽

Initial Value ◽

Runge Kutta

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An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions

Computer Physics Communications ◽

10.1016/s0010-4655(98)00088-5 ◽

1998 ◽

Vol 115 (1) ◽

pp. 1-8 ◽

Cited By ~ 136

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T.E. Simos

Keyword(s):

Numerical Integration ◽

Initial Value Problems ◽

Kutta Method ◽

Initial Value ◽

Runge Kutta Method ◽

Oscillating Solutions ◽

Exponentially Fitted ◽

Runge Kutta

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

Computers & Mathematics with Applications ◽

10.1016/0898-1221(93)90054-y ◽

1993 ◽

Vol 26 (12) ◽

pp. 7-15 ◽

Cited By ~ 23

Author(s):

T.E. Simos

Keyword(s):

Numerical Integration ◽

Initial Value Problems ◽

Second Order ◽

Initial Value ◽

Periodic Initial Value Problems ◽

Runge Kutta

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Block Runge-Kutta Methods for the Numerical Integration of Initial Value Problems in Ordinary Differential Equations Part II. The Stiff Case

Mathematics of Computation ◽

10.2307/2007369 ◽

1983 ◽

Vol 40 (161) ◽

pp. 193

Author(s):

J. R. Cash

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Numerical Integration ◽

Initial Value Problems ◽

Initial Value ◽

Runge Kutta

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Trigonometrically fitted three-derivative Runge–Kutta methods for solving oscillatory initial value problems

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.01.017 ◽

2018 ◽

Vol 330 ◽

pp. 103-117

Author(s):

Jiyong Li

Keyword(s):

Initial Value Problems ◽

Initial Value ◽

Oscillatory Initial Value Problems ◽

Runge Kutta

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Block Runge-Kutta Methods for the Numerical Integration of Initial Value Problems in Ordinary Differential Equations Part I. The Nonstiff Case

Mathematics of Computation ◽

10.2307/2007368 ◽

1983 ◽

Vol 40 (161) ◽

pp. 175 ◽

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Author(s):

J. R. Cash

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Numerical Integration ◽

Initial Value Problems ◽

Initial Value ◽

Runge Kutta

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

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10.1016/0377-0427(92)00114-o ◽

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Vol 51 (3) ◽

pp. 317-326 ◽

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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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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

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Keyword(s):

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Initial Value Problems ◽

Initial Value ◽

Nyström Method ◽

Nystrom Method ◽

Oscillatory Initial Value Problems ◽

Runge Kutta

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Modified Third Order Runge-Kutta Method based on Heronian Mean for Fuzzy Initial Value Problems and Hybrid Fuzzy Initial Value Problems

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Vol 15 (1) ◽

Keyword(s):

Initial Value Problems ◽

Kutta Method ◽

Initial Value ◽

Third Order ◽

Runge Kutta Method ◽

Runge Kutta ◽

Heronian Mean

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