Universal Newton's Iterative Method for Equation Solving with MATLAB Implementation

I have developed a universal MATLAB program implementing Newton's iterative method for equation solving, accompanied by validation result images. This program provides a comprehensive solution for solving various types of equations, including both single-variable and multi-variable systems, with guaranteed numerical accuracy through iterative convergence. The implementation features automated derivative calculation using symbolic differentiation for precise Jacobian matrix computation in multi-variable cases. The algorithm incorporates convergence checks and error handling to ensure reliable results across different equation types. A key enhancement is the integrated visualization capability that generates graphical representations of the solution process, displaying iteration convergence paths and final results through intuitive plots. This allows users to visually verify the solution validity and understand the convergence behavior. Users can benefit from significant time savings by simply inputting the equation expressions without requiring deep mathematical expertise. The program handles the complex computational aspects including initial value selection optimization, iteration step control, and precision tuning. The implementation uses MATLAB's symbolic math toolbox for accurate expression parsing and numerical computation for efficient iteration. This practical tool streamlines the equation-solving process through an intuitive interface combined with robust numerical methods, making it highly effective for educational, research, and engineering applications where reliable equation solutions are required.