TME 310 - Computational Physical Modeling

Bisection (root-finding)

Lorne Arnold, PhD, PE

University of Washington Tacoma

Root-finding methods

We have a few options:

1. Graphical methods
2. Bracketed methods
3. Open methods

Bracketed methods

Algorithms for searching within a specific range, bracketed by a lower and upper bound.

• Bisection method:
  • Look for the root at the range’s midpoint.
  • Decide which half contains the root and set that half as the new search range.
  • Repeat until tolerance is satisfied.

Bisection

Pros and cons (bisection)

Pros

• Fast (compared to graphical)
• Easy to implement
• If given valid bounds, it will find a solution

Cons

• Requires some knowledge of the root beforehand
• Assumes only one root

Bisection is great when you have a rough idea of where a single root is.