Interval Bisection
This module demonstrates the interval bisection method for solving a
nonlinear equation f(x) = 0 in one
dimension. Beginning with an initial interval in which the function
f has a change in sign, the interval is successively
halved until the solution has been isolated as accurately as desired.
The user selects a problem either by choosing a preset example or
typing in a desired function f(x) and initial
interval [a, b]. The successive steps of
interval bisection are then carried out sequentially by repeatedly
clicking on NEXT or on the currently highlighted step. The current
interval [a, b] and its computed midpoint
m are shown on the plot by labeled hash marks, and corresponding
function values are shown by bullets. In addition, all these values
are shown numerically in the table below. At each iteration, the
length of the interval is halved by taking either a =
m or b = m, depending on the
sign of f(m), and the process is then
repeated. The zero of the function, which always remains within the
retained interval, is eventually located as accurately as desired.
Reference: Michael T. Heath, Scientific Computing,
An Introductory Survey, 2nd edition, McGraw-Hill, New York,
2002. See Section 5.5.1, especially Algorithm 5.1 and Example 5.7.
Developers: Jeffrey Naisbitt and Michael Heath
Department of Computer Science