In this lab you will use a spreadsheet to illustrate the use of the Runge Kutta 4 method of estimating the value of the solution to an Ordinary Differential Equation with a given initial solution. You may also wish to print out the graph of the solution using ODE Architect (not required).
The problem: In July the hourly external temperature in
in a small town in south Georgia is given by
where
is the time in hours and midnight is
Use Newton's law of cooling to find the temperature inside a parked car at
noon if the temperature at midnight is
80
and the constant od proportionality is
Use 30 steps from midnight to noon.
Note: This time lapse (0,12) is longer, a lot longer, than you would normally want to use this method on to project an answer because the longer the time the larger the error. But it is more fun and does illustrate the method.
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