Contraction mapping method for root finding

There are graphically three steady currents through the tunnel diode with the given characteristic I = I(V) and a resistor R = 19.2 under the applied voltage source E = 1.4 (see the figure again). Their values can be computed with very good accuracy by using the standard MATLAB function fzero.m (type "help fzero" in MATLAB Command Window for more information). The voltage values for steady currents are

V1 = 0.172204        V2 = 0.532258        V3 = 0.795538

The contraction mapping method xk+1 = xk + f(xk) is stable for the second root V2 and is unstable for two other roots V1 and V3. The instability means that the method fails to find the roots V1 and V3, no matter how close your initial approximation is. Check this feature by entering different initial values for the contraction mapping method.

Enter an initial approximation of the root:


Possible initial values for your choice: 0.172, 0.173, 0.532, 0.533, 0.795 and 0.796. Notice that the method converges to the stable root V2 for any initial value between 0.172204 and 0.795538.