A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean

Rini Yanti; M Imran; Syamsudhuha

doi:doi:10.11648/j.acm.20140305.16

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A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean

Rini Yanti, M Imran, Syamsudhuha

Published in Applied and Computational Mathematics (Volume 3, Issue 5)

Received: 11 July 2014 Accepted: 12 September 2014 Published: 30 September 2014

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Abstract

We present a new third order Runge Kutta method based on linear combination of arithmetic mean, geometric mean and harmonic mean to solve a first order initial value problem. We also derive the local truncation error and show the stability region for the method. Moreover, we compare the new method with Runge Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results show that the performance of the new method is the same as known third order Runge-Kutta methods.

Published in	Applied and Computational Mathematics (Volume 3, Issue 5)
DOI	10.11648/j.acm.20140305.16
Page(s)	231-234
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Initial Value Problems, Runge Kutta Method, Arithmetic Mean, Harmonic Mean, Geometric Mean

References

[1]	O.Y. Ababneh and R. Rozita, New Third Order Runge Kutta Method Based on Contraharmonic Mean for Stiff Problems, Applied Mathematical Sciences, 3(2009), 365-376.
[2]	G. Dahlquist and A. Bjorck, Numerical Method, Prentice-Hall,Inc., New York, 1974.
[3]	D.J. Evans, 1989. New Runge-Kutta Methods For Initial Value Problems, Applied Mathematics Letter, 2(1989), pp.25--28.
[4]	S.K. Khattri, “Euler's Number and Some Means”, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2012), pp.369--377.
[5]	K.A. Ross, Elementary Analysis, Springer, New York, 1980.
[6]	L. P. Shampine, Numerical of Ordinary Diferential Equation, Chapman and Hall, New York, 1994.
[7]	A.G. Ujagbe, “On the Stability Analysis of a Geometric Mean 4th Order Runge-Kutta Formula, Mathematical Theory and Modelling, 3(2013), pp.76-91.
[8]	A.M. Wazwaz, “A Modified Third Order Runge-Kutta Method”, Applied Mathematics Letter, 3(1990), pp.123-125.

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APA Style

Rini Yanti, M Imran, Syamsudhuha. (2014). A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean. Applied and Computational Mathematics, 3(5), 231-234. https://doi.org/10.11648/j.acm.20140305.16

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ACS Style

Rini Yanti; M Imran; Syamsudhuha. A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean. Appl. Comput. Math. 2014, 3(5), 231-234. doi: 10.11648/j.acm.20140305.16

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AMA Style

Rini Yanti, M Imran, Syamsudhuha. A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean. Appl Comput Math. 2014;3(5):231-234. doi: 10.11648/j.acm.20140305.16

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@article{10.11648/j.acm.20140305.16,
  author = {Rini Yanti and M Imran and Syamsudhuha},
  title = {A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {5},
  pages = {231-234},
  doi = {10.11648/j.acm.20140305.16},
  url = {https://doi.org/10.11648/j.acm.20140305.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.16},
  abstract = {We present a new third order Runge Kutta method based on linear combination of arithmetic mean, geometric mean and harmonic mean to solve a first order initial value problem. We also derive the local truncation error and show the stability region for the method. Moreover, we compare the new method with Runge Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results show that the performance of the new method is the same as known third order Runge-Kutta methods.},
 year = {2014}
}

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TY  - JOUR
T1  - A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean
AU  - Rini Yanti
AU  - M Imran
AU  - Syamsudhuha
Y1  - 2014/09/30
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.16
DO  - 10.11648/j.acm.20140305.16
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 231
EP  - 234
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140305.16
AB  - We present a new third order Runge Kutta method based on linear combination of arithmetic mean, geometric mean and harmonic mean to solve a first order initial value problem. We also derive the local truncation error and show the stability region for the method. Moreover, we compare the new method with Runge Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results show that the performance of the new method is the same as known third order Runge-Kutta methods.
VL  - 3
IS  - 5
ER  -

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Author Information

Rini Yanti

Numerical Computing Group, Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia
M Imran

Numerical Computing Group, Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia
Syamsudhuha

Numerical Computing Group, Department of Mathematics, University of Riau, Pekanbaru 28293, Indonesia

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APA Style

Rini Yanti, M Imran, Syamsudhuha. (2014). A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean. Applied and Computational Mathematics, 3(5), 231-234. https://doi.org/10.11648/j.acm.20140305.16

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ACS Style

Rini Yanti; M Imran; Syamsudhuha. A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean. Appl. Comput. Math. 2014, 3(5), 231-234. doi: 10.11648/j.acm.20140305.16

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AMA Style

Rini Yanti, M Imran, Syamsudhuha. A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean. Appl Comput Math. 2014;3(5):231-234. doi: 10.11648/j.acm.20140305.16

Copy | Download

@article{10.11648/j.acm.20140305.16,
  author = {Rini Yanti and M Imran and Syamsudhuha},
  title = {A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {5},
  pages = {231-234},
  doi = {10.11648/j.acm.20140305.16},
  url = {https://doi.org/10.11648/j.acm.20140305.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.16},
  abstract = {We present a new third order Runge Kutta method based on linear combination of arithmetic mean, geometric mean and harmonic mean to solve a first order initial value problem. We also derive the local truncation error and show the stability region for the method. Moreover, we compare the new method with Runge Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results show that the performance of the new method is the same as known third order Runge-Kutta methods.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - A Third Runge Kutta Method Based on a Linear Combination of Arithmetic Mean, Harmonic Mean and Geometric Mean
AU  - Rini Yanti
AU  - M Imran
AU  - Syamsudhuha
Y1  - 2014/09/30
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.16
DO  - 10.11648/j.acm.20140305.16
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 231
EP  - 234
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140305.16
AB  - We present a new third order Runge Kutta method based on linear combination of arithmetic mean, geometric mean and harmonic mean to solve a first order initial value problem. We also derive the local truncation error and show the stability region for the method. Moreover, we compare the new method with Runge Kutta method based on arithmetic mean, geometric mean and harmonic mean. The numerical results show that the performance of the new method is the same as known third order Runge-Kutta methods.
VL  - 3
IS  - 5
ER  -

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