Lecture 12 Presentation and Examples FALL2011

Lecture 12 Presentation and Examples FALL2011 -...

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Organization of Differential Equations 1

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Numerical Solutions to 1 st Order ODEs Prof. Dragan Djurdjanovic ME 218 Fall 2011 2
Euler’s Method 3 Actual solution is y(0.4)=-0.81096

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Heun’s Method Equivalent to Taylor Series Expansion up to (and including) 2 nd order terms (involves numerical approximations of 2 nd order derivatives) 4 Actual solution is y(0.4)=-0.81096
4 th Order Runge-Kutta (RK) Method Equivalent to Taylor Series Expansion up to (and including) 4 th order terms (involves numerical approximations of 4 th order derivatives) 5

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4 th Order Runge Kutta Method 6 Equivalent to Taylor Series Expansion up to (and including) 4 th order terms (involves numerical approximations of 4 th order derivatives)
Choice of Step Sizes for Numerical Solution to 1 st Order ODEs 7

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Banking Problem for Numerical Solutions to 1 st Order ODEs Prof. Dragan Djurdjanovic ME 218 Fall 2011 8
A sum of P= \$5,000 (P) is invested in European sovereign bongs The interest on the bond is r = 5% per annum (also try for 7 % in Italy). Assume that additional funds are invested continuously at the rate of c = \$1,000 per annum What is the value of the investment at the end of k = 10 years, assuming that the interest is compounded continuously ? 9

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This note was uploaded on 12/14/2011 for the course ME 218 taught by Professor Unknown during the Fall '08 term at University of Texas.

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Lecture 12 Presentation and Examples FALL2011 -...

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