Nonlinear Equation Solver with MATLAB Graphical User Interface

Abstract

Nonlinear systems of equations, which is common in scientific and engineering fields, pose a significant difficulty because they may have numerous solutions and are complicated to be numerically solved. This study aims to improve the effectiveness and availability of solving these systems by creating a MATLAB Graphical User Interface (GUI) to compare different iterative methods. The GUI makes it easier to evaluate algorithm performance by providing a more accessible interface to input nonlinear functions, their Jacobians, and also their respective initial approximations. The article evaluates the differences and similarities of four commonly used iterative methods: Newton, Broyden, BFGS, and Steepest Descent. A set of ten typical nonlinear test functions were created specifically as a benchmark suite for assessing methods in different situations. Thorough testing and analysis helped determine the advantages and disadvantages of each approach, offering insights into their suitability for different problem characteristics. Researchers and practitioners who have tried to analyse and contrast the reliabilities of iterative methods in solving nonlinear systems may discover the MATLAB GUI to be beneficial. By utilizing a visual and interactive interface, the GUI allows users to gain deep understanding.

Keywords

• Matlab
• Nonlinear function
• System of Nonlinear equations
• Nonlinear equations
• Iterative Algorithms