Applied and Computational Mathematics

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

Received: 26 September 2016    Accepted: 03 March 2017    Published: 04 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.

DOI 10.11648/j.acm.20170604.11
Published in Applied and Computational Mathematics (Volume 6, Issue 4, August 2017)
Page(s) 167-170
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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), 2024. 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.
Author Information
  • Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria

  • Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria

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    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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    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://download.sciencepg.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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