python crash course 6: fixed point iterations

We discuss the fundamentals of fixed point iterations and their utility in solving transcendental equations. In particular, we obtain the cobweb plot of convergence towards a root when the slope of the function is less than one. We demonstrate the divergence of the process when the slope of the function is larger than one. The method may be adapted for various nonlinear equations as well.

The programming is done in python (Spyder 4 IDE). Python along with scipy, numpy, and matplotlib may be considered as a viable and free alternative to MATLAB. Those acquainted with MATLAB will find the learning curve quite mild.