EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 4, Problem 8P
Use a centered difference approximation of
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Consider the following ODE in time (from Homework 6). Integrate in time using 4th order Runge-Kutta
method. Compare this solution with the finite difference and analytical solutions from Homework 6.
4 25
u(0)=0
(a) Use At = 0.2 up to a final time t = 1.0.
(b) Use At=0.1 up to a final time t = 1.0.
0
(0)=2
(c) Discuss the difference in the two solutions of parts (a) and (b). Why are they so different?
Circle final answer
Question: Which series helps us to derive the discretized form of the governing equations?
Remember to circle final answer
4. If all
variables of
choose the
a stream
are
correct answer
dependent
of time it is
said to be
in: (a)
Steady flow
(b)
Unsteady
flow (c)
Uniform
flow (d)
Closed
flow (e)
Constant
flow
5. In an
irreversible
process,
there is a:
(a) loss of
heat (b) No O
loss of heat
(c) Gain of
heat (d) No
gain of
heat
Chapter 4 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 4 - The following series can be used to approximate...Ch. 4 - 4.2 The Maclaurin series expansion for cos x...Ch. 4 - 4.3 Perform the same computation as in Prob. 4.2,...Ch. 4 - 4.4 The Maclaurin series expansion for the...Ch. 4 - 4.5 Use zero- through third-order Taylor series...Ch. 4 - 4.6 Use zero- through fourth-order Taylor series...Ch. 4 - Use forward and backward difference approximations...Ch. 4 - 4.8 Use a centered difference approximation of to...Ch. 4 - 4.9 The Stefan-Boltzmann law can be employed to...Ch. 4 - Repeat Prob. 4.9 but for a copper sphere with...
Ch. 4 - Recall that the velocity of the falling...Ch. 4 - 4.12 Repeat Prob. 4.11 with.
Ch. 4 - 4.13 Evaluate and interpret the condition numbers...Ch. 4 - Employing ideas from Sec. 4.2, derive the...Ch. 4 - Prove that Eq. (4.4) is exact for all values of x...Ch. 4 - Mannings formula for a rectangular channel can be...Ch. 4 - If |x|1, it is known that 11x=1+x+x2+x3+ Repeat...Ch. 4 - A missile leaves the ground with an initial...Ch. 4 - To calculate a planets space coordinates, we have...Ch. 4 - 4.20 Consider the function on the interval . Use...Ch. 4 - Derive Eq. (4.31).Ch. 4 - 4.22 Repeat Example 4.8, but for .
Ch. 4 - 4.23 Repeat Example 4.8, but for the forward...Ch. 4 - 4.24 Develop a well-structured program to compute...
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