Introduction to Engineering and Scientific Computing with Python

7 Solving Single Algebraic Equations

DOI: 10.1201/9781003256861-7

Chapter Objectives

• Learn bracketing methods for solving single equations, both bisection and false position.
• Implement the bracketing methods by developing Python functions.
• Understand the background behind open methods for solving single equations, including the Newton-Raphson method and the secant method.
• Develop Python functions to implement the open methods.
• Learn about a hybrid, bracketing/open method, Brent’s method, and how to use the built-in brentq function from the SciPy optimize module.
• See how some equations occur naturally in a successive substitution or circular format, x = g(x), and understand the characteristics that govern convergence of fixed-point iteration. ...