Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs

S. O. Imoni; M. N. O. Ikhile

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2014)

  • Volume: 53, Issue: 2, page 53-69
  • ISSN: 0231-9721

Abstract

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For initial value problem (IVPs) in ordinary second order differential equations of the special form y ' ' = f x , y possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem reduced to first-order system.

How to cite

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Imoni, S. O., and Ikhile, M. N. O.. "Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 53.2 (2014): 53-69. <http://eudml.org/doc/262164>.

@article{Imoni2014,
abstract = {For initial value problem (IVPs) in ordinary second order differential equations of the special form $y^\{\prime \prime \}=f\left(x,y\right)$ possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem reduced to first-order system.},
author = {Imoni, S. O., Ikhile, M. N. O.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Initial value problems; Runge–Kutta–Nystrom pairs; zero dissipative; initial value problems; Runge-Kutta-Nystrom pairs; zero dissipative; oscillating solutions; numerical result},
language = {eng},
number = {2},
pages = {53-69},
publisher = {Palacký University Olomouc},
title = {Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs},
url = {http://eudml.org/doc/262164},
volume = {53},
year = {2014},
}

TY - JOUR
AU - Imoni, S. O.
AU - Ikhile, M. N. O.
TI - Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2014
PB - Palacký University Olomouc
VL - 53
IS - 2
SP - 53
EP - 69
AB - For initial value problem (IVPs) in ordinary second order differential equations of the special form $y^{\prime \prime }=f\left(x,y\right)$ possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem reduced to first-order system.
LA - eng
KW - Initial value problems; Runge–Kutta–Nystrom pairs; zero dissipative; initial value problems; Runge-Kutta-Nystrom pairs; zero dissipative; oscillating solutions; numerical result
UR - http://eudml.org/doc/262164
ER -

References

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