The `vpasolve` function in MATLAB is part of the Symbolic Math Toolbox and is used for solving systems of equations symbolically. It leverages various algorithms and techniques from numerical analysis and symbolic computation to find solutions to equations or systems of equations.
Internally, `vpasolve` uses a combination of numerical and symbolic methods to solve equations. It employs numerical methods, such as interval arithmetic and root-finding algorithms, to compute numerical approximations of solutions. Additionally, it utilizes symbolic techniques, including equation manipulation and simplification, to handle symbolic expressions and equations.
The specific algorithms employed by `vpasolve` can vary depending on the nature of the equations being solved. It may utilize methods like Newton's method, interval arithmetic, bisection, or other numerical techniques to find approximate solutions. Symbolic techniques, such as Groebner basis computations or resultants, may also be used for solving polynomial equations.
To conclude `vpasolve` combines numerical and symbolic approaches to provide a flexible and robust solver for systems of equations in MATLAB.
You can read more about vpasolve here: Solve symbolic equations numerically - MATLAB vpasolve (mathworks.com)
