Newton's Method for Nonlinear Equations with Symbolic Computation

This program implements Newton's method for solving nonlinear equations using symbolic computation techniques in MATLAB. It accepts parametric algebraic expressions as direct input, eliminating the need to manually separate individual matrices. The key implementation features automatic derivative calculation through symbolic differentiation, which computes the Jacobian matrix required for Newton's iteration formula. This approach significantly improves computational efficiency while preventing errors that commonly occur during manual derivative calculations. The algorithm operates by symbolically parsing the input equations, constructing the corresponding Jacobian matrix through automated differentiation, and executing iterative updates using the Newton-Raphson formula x_{k+1} = x_k - J(x_k)^{-1}F(x_k). The program includes detailed output capabilities that display intermediate results at each iteration step, providing users with comprehensive debugging and analysis tools to monitor convergence behavior and verify solution accuracy throughout the computational process.