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Newton’s Method for Solving Non-Linear System of Algebraic Equations (NLSAEs) with MATLAB/Simulink® and MAPLE®
American Journal of Mathematical and Computer Modelling
Volume 2, Issue 4, November 2017, Pages: 117-131
Received: Nov. 25, 2017; Accepted: Dec. 7, 2017; Published: Jan. 3, 2018
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Aliyu Bhar Kisabo, Department of Dynamics & Control System, Centre for Space Transport & Propulsion (CSTP), Lagos, Nigeria
Nwojiji Cornelius Uchenna, Department of Marine Engineering, Fleet Support Unit BEECROFT, Lagos, Nigeria
Funmilayo Aliyu Adebimpe, Department of Chemical Propulsion System, Centre for Space Transport & Propulsion (CSTP), Lagos, Nigeria
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Interest in Science, Technology, Engineering and Mathematics (STEM)-based courses at tertiary institution is on a steady decline. To curd this trend, among others, teaching and learning of STEM subjects must be made less mental tasking. This can be achieved by the aid of technical computing software. In this study, a novel approach to explaining and implementing Newton’s method as a numerical approach for solving Nonlinear System of Algebraic Equations (NLSAEs) was presented using MATLAB® and MAPLE® in a complementary manner. Firstly, the analytical based computational software MAPLE® was used to substitute the initial condition values into the NLSAEs and then evaluate them to get a constant value column vector. Secondly, MAPLE® was used to obtain partial derivative of the NLSAEs hence, a Jacobean matrix. Substituting initial condition into the Jacobean matrix and evaluating resulted in a constant value square matrix. Both vector and matrix represent a Linear System of Algebraic Equations (LSAEs) for the related initial condition. This LSAEs was then solved using Gaussian Elimination method in the numerical-based computational software of MATLAB/Simulink®. This process was repeated until the solution to the NLSAEs converged. To explain the concept of quadratic convergence of the Newton’s method, power function of degree 2 (quad) relates the errors and successive errors in each iteration. This was achieved with the aid of Curve Fitting Toolbox of MATLAB®. Finally, a script file and a function file in MATLAB® were written that implements the complete solution process to the NLSAEs.
Newton’s Method, MAPLE®, MATLAB®, Non-Linear System of Algebraic Equations
To cite this article
Aliyu Bhar Kisabo, Nwojiji Cornelius Uchenna, Funmilayo Aliyu Adebimpe, Newton’s Method for Solving Non-Linear System of Algebraic Equations (NLSAEs) with MATLAB/Simulink® and MAPLE®, American Journal of Mathematical and Computer Modelling. Vol. 2, No. 4, 2017, pp. 117-131. doi: 10.11648/j.ajmcm.20170204.14
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Lyn Haynes (2008). Studying Stem? What are the Barriers. A Literature Review of the Choices Students Make. A Fact-file Provided By The Institution of Engineering and Technology
Frank Y. Wang (2015). Physics with MAPLE: The Computer Algebra Resource for Mathematical Methods in Physics. ISBN: 3-527-40640-9
Ralph E. White and Venkat R. Subramanian (2010). Computational Methods in Chemical Engineering with MAPLE. ISBN 978-3-642-04310-9
Robin C. and Murat T. (1994). Engineering Explorations with MAPLE. ISBN: 0-15-502338-7
George Z. V and Peter I. K (2005). Mechanics of Composite Materials with MATLAB, ISBN-10 3-540-24353-4
Wndy L. M and Angel R. M (2002). Computational Statistics Handbook with MATLAB. ISBN 1-58488-229-8
Bassem R. M (2000). Radar Systems Analysis and Design Using MATLAB. ISBN 1-58488-182-8
Glyn James et al (2015). Modern Engineering Mathematics, ISBN: 978-1-292-08073-4
Linge S., Langtangen H. P. (2016) Solving Nonlinear Algebraic Equations. In: Programming for Computations - MATLAB/Octave. Texts in Computational Science and Engineering, vol 14. Springer, Cham. ISBN 978-3-319-32452-4.
Burden, Richard L. and J. Douglas Faires, (2010). Numerical Analysis, 9th Ed., Brooks Cole, ISBN 0538733519
Robin Carr and Murat Tanyel (1994). Engineering Exploration with MAPLE. ISBN: 0-15-502338-7
MAPLE User Manual Copyright © Maplesoft, a division of Waterloo Maple Inc.1996-2009. ISBN 978-1-897310-69-4
Harold Klee and Randal Allen (2011). Simulation of Dynamic Systems with MATLAB and Simulink, ISBN -13: 978-1-4398-3674-3
O. B euchre and M. Week (2006). Introduction to MATLAB & Simulink: A project Approach, Third Edition. ISBN: 978-1-934015-04-9
Steven T. Karris (2006). Introduction to Simulink with Engineering Applications, ISBN 978-0-9744239-8-2
Cheney, Ward and David Kincaid, (2007) Numerical Mathematics and Computing, 6th Ed., Brooks Cole, 2007, ISBN 0495114758
Kincaid, David and Ward Cheney, (2002). Numerical Analysis: Mathematics of Scientific Computing, Vol. 2, 2002, ISBN 0821847880
Curve Fitting Toolbox™ User’s Guide (2014). The Math Works, Inc.
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