This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# StepMonitor

 StepMonitoris an option for iterative numerical computation functions that gives an expression to evaluate whenever a step is taken by the numerical method used.
• The option setting is normally given as StepMonitor:>expr.
• The is used instead of to avoid expr being immediately evaluated.
• Whenever expr is evaluated, all variables in the numerical computation are assigned their current values.
• Block is effectively used.
Monitor steps taken for a numerical minimization with FindMinimum:
Count steps:
Use Reap and Sow to collect step data:
Show steps on a plot of the function:
Monitor steps taken for a numerical minimization with FindMinimum:
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Count steps:
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Use Reap and Sow to collect step data:
 Out[1]=
Show steps on a plot of the function:
 Out[2]=
 Scope   (4)
Monitor the solution progress when solving the sine-Gordon PDE:
Monitor steps taken to numerically solve a system of equations:
Show steps on a surface plot of the functions:
Steps in parameter space for a nonlinear fit:
Sequence of plots showing the evolution of the model over the steps:
Plot the spatial (x) solution for time (t) steps used numerically solving a PDE with NDSolve:
Show the steps with a surface plot of the solution:
 Applications   (4)
Show how precision is adapted for high-precision root finding:
The quadratic convergence of Newton's method allows eventual precision doubling at each step:
Investigate steps and evaluations for a numerical minimization:
Show evaluations in red, steps in yellow, and the final point in green:
Get step sizes for the numerical solution of an ODE with NDSolve:
Show the solution and step size as a function of t:
Compare steps, evaluations, and timing for different ODE integration methods in NDSolve:
New in 5