Monitor
NIntegrate, with steps along the

axis and evaluation points on the

axis:
Monitor
NDSolve using an extrapolation method:
Monitor
NDSolve solving the sine-Gordon PDE:
Steps in parameter space for a nonlinear fit:
Monitor the evolution of the model over the steps with a graph:
Implement a simple LU decomposition with a slowdown parameter

:
Monitor an algorithm animation using
MatrixForm or
MatrixPlot: