which method is best and why. Bisection method and Regula falsi method
Answers
the error for false position decreases much faster than for bisection because of the more efficent scheme root locations in the false -position method .
Case Where Bisection Is Preferable to False Position
Problem Statement. Use bisection and false position to locate the root of
f(x) 5 x10 2 1
between x 5 0 and 1.3.
Solution. Using bisection, the results can be summarized as
Iteration xl xu xr -
a (%) -
t (%)
1 0 1.3 0.65 100.0 35
2 0.65 1.3 0.975 33.3 2.5
3 0.975 1.3 1.1375 14.3 13.8
4 0.975 1.1375 1.05625 7.7 5.6
5 0.975 1.05625 1.015625 4.0 1.6
Thus, after fi ve iterations, the true error is reduced to less than 2 percent. For false
position, a very different outcome is obtained:
Iteration xl xu xr -
a (%) -
t (%)
1 0 1.3 0.09430 90.6
2 0.09430 1.3 0.18176 48.1 81.8
3 0.18176 1.3 0.26287 30.9 73.7
4 0.26287 1.3 0.33811 22.3 66.2
5 0.33811 1.3 0.40788 17.1 59.2