Solving Nonlinear Equations Using Newton's Iteration Method with MATLAB Implementation

This MATLAB source program implements Newton's iteration method for solving nonlinear equations. Newton's method is an efficient numerical computation technique for finding solutions to nonlinear equation systems. The core algorithm operates by iteratively refining approximations until convergence to the solution is achieved. In this MATLAB implementation, we first define the system of equations as functional expressions, then apply Newton's iterative methodology. The program specifically utilizes matrix differentiation and matrix inversion techniques to compute the iterative formula central to Newton's method. Key computational steps include calculating the Jacobian matrix through symbolic or numerical differentiation and implementing the Newton update step: x_{k+1} = x_k - J^{-1}(x_k) * F(x_k), where J represents the Jacobian matrix and F denotes the system functions. Finally, the solution results are output and visualized through graphical representations, facilitating comprehensive analysis and interpretation of numerical computation outcomes. Convergence criteria and iteration limits are implemented to ensure computational efficiency and solution accuracy.