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

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.