Volume 2, Issue 4, November 2017, Page: 117-131

Newton’s Method for Solving Non-Linear System of Algebraic Equations (NLSAEs) with MATLAB/Simulink

^{®}and MAPLE^{®}
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

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

Received: Nov. 25, 2017;
Accepted: Dec. 7, 2017;
Published: Jan. 3, 2018

DOI: 10.11648/j.ajmcm.20170204.14 View 1118 Downloads 75

Abstract

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.Keywords

Newton’s Method, MAPLE

^{®}, MATLAB^{®}, Non-Linear System of Algebraic EquationsTo 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.20170204.14Copyright

Copyright © 2017 Authors retain the copyright of this article.

This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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