root equations methods

13
ROOTS OF EQUATIONS

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  • 1. ROOTS OF EQUATIONS

2. GRAPHICAL METHODS
In these methods, what is sought is to plot the graph of y = f (x). The point where cutting the abscissa (x) is the root. These methods although very general, have their drawbacks.


3. INTERVAL METHODS
4. It is a simple, time-consuming and has linear convergence, and is performed as follows:
1. Choose the initial values lower Xi and upper Xs.
2. The first approximation to the root Xr is determined as:
=
3. Calculate F (Xi), F (Xr) to determine in which subinterval the root lies.



BISECTION METHODS
5. 4.Then:
a)If F (Xi) * F (Xr) 0, the root is in the upper subinterval, then:
Xr= Xi
5.Then, repeat the pointtwo y when Error