Ps2 - 2.23 Hydrofoils Propellers Homework Assignment#2 Assigned Fri Feb 23 2007 Due Fri Mar 2 2007 1 Perform a numerical integration on the

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2.23 Hydrofoils & Propellers Homework Assignment #2 Assigned: Fri. Feb. 23, 2007 Due: Fri. Mar 2, 2007 1) Perform a numerical integration on the following function I = 0 5 cos 2 ( x ) + 3 e x + x 3 dx From x=0 to x=5 Using: a) Trapeziodal rule with 100 steps b) Trapezoidal rule with 200 steps c) Above results + Richardson extrapolation equation (This is a 2 iteration Romberg integration) d) Using a 2 point Gaussian Quadrature method 2) Implement an Euler method solution in Matlab code to solve the differntial equation: di dt = 1.5 + 2.5 i a) Compute and plot the exact solution of the integral from time t=o to t=3. b) Implement a central difference Euler solution ti I as a function of time with intial conditions i=0 at t=0 up to a time of t=3. c) Run the euler solution for various stepsizes from 0.2 to .002 d) Produce a plot showing the exact solution and a few different stepsize solutions showing convergence with stepsize. 3)
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.23 taught by Professor Pauld.sclavounos during the Spring '07 term at MIT.

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Ps2 - 2.23 Hydrofoils Propellers Homework Assignment#2 Assigned Fri Feb 23 2007 Due Fri Mar 2 2007 1 Perform a numerical integration on the

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