nonlinear_bisection.pdf

Nonlinear equations:

The bisection method

MATH2070: Numerical Methods in Scientific Computing I

Location: http://people.sc.fsu.edu/∼jburkardt/classes/math2070 2019/nonlinear bisection/nonlinear bisection.pdf

Why does a function cross the axis? To get to the other sign!

Mathematics provides methods for finding solutions to some algebraic equations like x

2

− 2x − 15 = 0.

However, for most equations with any kind of complication, there is no way to come to an exact solution for

x. The bisection method provides a computational path to solving a nonlinear equation.

Kepler’s equation comes from an astronomical problem. It relates an important quantity, E, the eccentric

anomaly of an orbit, to two easily measured items, the mean anomaly M and the orbital eccentricity e: