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The task

Bisection Method

Of Solving Nonlinear Equations

Here the bisection method algorithm is applied to generate the values of the roots, true error, absolute relative true error, approximate error, absolute relative approximate error, and the number of significant digits at least correct in the estimated root as a function of number of iterations.

The task

The "true" solution is taken as the solution that Mathcad's numerical root solver obtains. This is a decent assumption because their subroutines have been professionally written. You must take caution, however, because Mathcad's "root" function might be finding another of the functions roots. For the rest of the sheet to be correct, you need to ensure that xtrueis the root that you are attempting to find.

This can be altered by changing the value of xguessabove. It is also possible that Mathcad's tolerance might not be accurate enough. You can change this by redefining the TOC constant.

root(f(var1, var2,...),var1, [a, b]) – returns the value of var1 lying between a and b at which the function f equal to zero.