Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra

Mustafa A.; M. M. Hamza

doi:doi:10.11648/j.acm.20170604.11

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Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra

Mustafa A., M. M. Hamza

Published in Applied and Computational Mathematics (Volume 6, Issue 4)

Received: 26 September 2016 Accepted: 3 March 2017 Published: 4 July 2017

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Abstract

In this paper, a well-known computer algebra system (CAS) was considered for the derivation of Numerical method for the solution of initial value problems. This was achieved by the use of maple software. Numerical methods were derived through Lagrange interpolation method. Both the implicit and explicit method was derived with the help of the Computer algebra system. In particular, a review of Maple’s functional role in the derivation of numerical methods was also presented. The main challenge was that the efficient handling and simplifying of very long expressions, which was met by the power of Maple’s build-in functionality. The use of the maple procedure had significantly reduced the errors and hence improved efficiency in derivation of higher order Adams Methods.

Published in	Applied and Computational Mathematics (Volume 6, Issue 4)
DOI	10.11648/j.acm.20170604.11
Page(s)	167-170
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), 2017. Published by Science Publishing Group

Keywords

Computer Algebra, Lagrange, Initial Value, Linear Multistep Method

References

[1]	Maplesoft, Getting Started Guide, Waterloo: htttp://www.maplesoft.com, 2007.
[2]	T. Yamaguchi, Mathematical methods with maple., Universal Academy press, inc, 2005, pp. 151-155.
[3]	D. a. H. S. Dennis, “Lecture note on numerical Analysis.,” pp. 74-79, 2002.
[4]	P. a. S. Kloeden, “Construction of stochastic numerical schemes through Maple,” Maple Technical Newsletter, 1993.
[5]	W. Kendell, Computer algebra and stochastic calculus, Notices Amer. Math.science, 1990, pp. 1254-1256.
[6]	H. A., Introduction to maple, third edition ed., Germany: Sringer-Verlag, 2003.
[7]	J. Lambert, Numerical methods for ordinary Differential equations:The initial value problem, 2nd ed., London: Wiley, 2000.
[8]	P. Corke, “An automated symbolic and numeric procedure for manipulating rigid-body dynamical significance analysis and simplification,” vol. 12, pp. 1018-1023, 1996.
[9]	J. Butcher, Numerical Methods for ordinary differential equations, Chchester, England: Wiley and son's, 2008.
[10]	J. Wallen, “On robot modelling using Maple.,” Universitytext.sweden, sweden, 2007.

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APA Style

Mustafa A., M. M. Hamza. (2017). Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra. Applied and Computational Mathematics, 6(4), 167-170. https://doi.org/10.11648/j.acm.20170604.11

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ACS Style

Mustafa A.; M. M. Hamza. Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra. Appl. Comput. Math. 2017, 6(4), 167-170. doi: 10.11648/j.acm.20170604.11

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AMA Style

Mustafa A., M. M. Hamza. Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra. Appl Comput Math. 2017;6(4):167-170. doi: 10.11648/j.acm.20170604.11

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@article{10.11648/j.acm.20170604.11,
  author = {Mustafa A. and M. M. Hamza},
  title = {Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {4},
  pages = {167-170},
  doi = {10.11648/j.acm.20170604.11},
  url = {https://doi.org/10.11648/j.acm.20170604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170604.11},
  abstract = {In this paper, a well-known computer algebra system (CAS) was considered for the derivation of Numerical method for the solution of initial value problems. This was achieved by the use of maple software. Numerical methods were derived through Lagrange interpolation method. Both the implicit and explicit method was derived with the help of the Computer algebra system. In particular, a review of Maple’s functional role in the derivation of numerical methods was also presented. The main challenge was that the efficient handling and simplifying of very long expressions, which was met by the power of Maple’s build-in functionality. The use of the maple procedure had significantly reduced the errors and hence improved efficiency in derivation of higher order Adams Methods.},
 year = {2017}
}

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T1  - Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra
AU  - Mustafa A.
AU  - M. M. Hamza
Y1  - 2017/07/04
PY  - 2017
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AB  - In this paper, a well-known computer algebra system (CAS) was considered for the derivation of Numerical method for the solution of initial value problems. This was achieved by the use of maple software. Numerical methods were derived through Lagrange interpolation method. Both the implicit and explicit method was derived with the help of the Computer algebra system. In particular, a review of Maple’s functional role in the derivation of numerical methods was also presented. The main challenge was that the efficient handling and simplifying of very long expressions, which was met by the power of Maple’s build-in functionality. The use of the maple procedure had significantly reduced the errors and hence improved efficiency in derivation of higher order Adams Methods.
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Author Information

Mustafa A.

Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
M. M. Hamza

Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria

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APA Style

Mustafa A., M. M. Hamza. (2017). Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra. Applied and Computational Mathematics, 6(4), 167-170. https://doi.org/10.11648/j.acm.20170604.11

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ACS Style

Mustafa A.; M. M. Hamza. Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra. Appl. Comput. Math. 2017, 6(4), 167-170. doi: 10.11648/j.acm.20170604.11

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AMA Style

Mustafa A., M. M. Hamza. Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra. Appl Comput Math. 2017;6(4):167-170. doi: 10.11648/j.acm.20170604.11

Copy | Download

@article{10.11648/j.acm.20170604.11,
  author = {Mustafa A. and M. M. Hamza},
  title = {Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {4},
  pages = {167-170},
  doi = {10.11648/j.acm.20170604.11},
  url = {https://doi.org/10.11648/j.acm.20170604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170604.11},
  abstract = {In this paper, a well-known computer algebra system (CAS) was considered for the derivation of Numerical method for the solution of initial value problems. This was achieved by the use of maple software. Numerical methods were derived through Lagrange interpolation method. Both the implicit and explicit method was derived with the help of the Computer algebra system. In particular, a review of Maple’s functional role in the derivation of numerical methods was also presented. The main challenge was that the efficient handling and simplifying of very long expressions, which was met by the power of Maple’s build-in functionality. The use of the maple procedure had significantly reduced the errors and hence improved efficiency in derivation of higher order Adams Methods.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra
AU  - Mustafa A.
AU  - M. M. Hamza
Y1  - 2017/07/04
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170604.11
DO  - 10.11648/j.acm.20170604.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 167
EP  - 170
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170604.11
AB  - In this paper, a well-known computer algebra system (CAS) was considered for the derivation of Numerical method for the solution of initial value problems. This was achieved by the use of maple software. Numerical methods were derived through Lagrange interpolation method. Both the implicit and explicit method was derived with the help of the Computer algebra system. In particular, a review of Maple’s functional role in the derivation of numerical methods was also presented. The main challenge was that the efficient handling and simplifying of very long expressions, which was met by the power of Maple’s build-in functionality. The use of the maple procedure had significantly reduced the errors and hence improved efficiency in derivation of higher order Adams Methods.
VL  - 6
IS  - 4
ER  -

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