# Department of Mechanical Engineering ME 2173: Numerical MethodsSpring 2022 MATLAB Project 3 Submission requirements: · Publish your script on PDF with the publish command. Submit your PDF file AND...

Department of Mechanical Engineering
ME 2173: Numerical Methods    Spring 2022
MATLAB        Project 3
Submission requirements:
· Publish your script on PDF with the publish command. Submit your PDF file AND the Matlab file (.m) to Blackboard.
· Multiple submissions will be allowed before deadline.
· Late submissions will follow class course rules.
· Point will be deducted for excessive output.
· Codes that do not run will not be graded.
Experimental Data:
The data in Data.csv represents recorded voltage vs. time. Time (s) is the first column and voltage (V) is the second. Use the data to determine the most suitable regression to model the data. Use this regression alongside interpolation in order to estimate the voltage at t=2.35 s and t=8.84 s.
· Use readmatrix to import the data into Matlab.
· Fit the following regressions models to the data:
· Linear:
· Exponential:
· Power:
· Saturation Growth:
· Generate one plot with the data and the 5 regression curves. For the data use a linestyle that does not connect the markers. Include title, axis labels and a legend. Based on the plot which regression model best describes the data?
· Display the regression coefficients and the equation for the model chosen in the previous part.
· For t=2.35 s and t=8.84 s estimate the Voltage using:
· Linear interpolation via linear systems.
· Quadratic interpolation via linear systems.
· Be mindful of which points you include for the linear systems interpolation.
Estimate the solution of the following IVP on the interval t=1 to t=5:
Use Euler method and RK4 with a timestep of 0.1s. Compare your solutions to the results of using ode45 in Matlab as well as the analytical solution:
· Display one plot with 4 curves (Euler, RK4, ode45 and analytical solution)
· Display the percent difference between the 3 solution methods and the analytical solution at t=2,3,4,5 seconds (12 numbers total) and explain the changes in e
or.
· Display the total computation time for the 3 solution methods (Euler,RK4, ode45)
· Which method performed the best. (Time and E
or should be included in this discussion)