Lecture 13 Presentation and Example

# Lecture 13 Presentation and Example - Simultaneous1st Order...

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Click to edit Master subtitle style Simultaneous1st Order ODE-s Higher Order ODE-s Boundary Value Problems (ODE-s) Prof. Dragan Djurdjanovic ME 218 Fall 2008 11

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Recapitulation: Euler’s Method 22
Recapitulation: Heun’s Method Equivalent to Taylor Series Expansion up to (and including) 2nd order terms (involves numerical approximations of 2nd order derivatives) 33

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Recapitulation: 4th Order Runge-Kutta (RK) Method Equivalent to Taylor Series Expansion up to (and including) 4th order terms (involves numerical approximations of 4th order derivatives) 44
Selection of a Step Size n Select a random step size, h, if not specified. n Tabulate the results obtained using that step size n Choose a lower step size, say about 0.2h n Run the iteration scheme and tabulate the results n Check new results against the previous results, and obtain the difference. ¡ If the difference is less than a specified tolerance limit, convergence has been achieved with regards the step size, and h is an appropriate size, keeping in mind computational

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## This note was uploaded on 06/23/2011 for the course ME 218 taught by Professor Unknown during the Fall '08 term at University of Texas at Austin.

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Lecture 13 Presentation and Example - Simultaneous1st Order...

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