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fall2010Quiz2Solutions

# fall2010Quiz2Solutions - ChBE 2120 Fall 2010 Quiz 2 NAME On...

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Unformatted text preview: ChBE 2120, Fall 2010, Quiz 2 NAME: On this sheet, give only the ﬁnal answers for each question in the box provided — no partial credit. The midpoint method for integrating ODEs is deﬁned as: h y”; = yt- + -f(tL-,yz) 2 yi+1= yi+hf(ti+y11y 1) +2+2 1. Using the midpoint method, integrate the yfollowing differential equatiOn from 0 to 1, with a step size of l, and an initial value of 0): #.Q:—x{12—yx— 2 12mm: 13 Answer)”: Q 2. True or false: The deﬁnition of the midpoint method suggests that integrating with the midpoint method is identical to integrating with the Euler method with half the step size. 3. Which of the following is the best indicator of a stiff differential equation? A) Nonlinear terms in t B) Nonlinear terms in y or its time derivatives C) A second or higher order differential equation/system of equations D) Coefﬁcients that are orders of magnitude different from each other E) Negative coefﬁcients in exponential terms dzw dw 4. Censider the following 2nd order ODE: Er? = 71-; — COS W + x Express this ODE as a system of coupled lSt order ODEs in terms of x and two new “variables”, and y;. i U} EM" 13537::de 77‘ ﬁg? d 5 : ﬂiylﬂrz AWAY: 3 32.6653: +176 ...
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