E NGR 8103: C OMPUTATIONAL E NGINEERING
Problem Set 4 (due Wednesday in my mailbox by 4pm, 9/25)
Questions:
1. Show that when the fourth-order Runge-Kutta method is applied to the problem x = 2x, the formula
for advancing this solution will be
4
2
x(t + h
E NGR 8103: C OMPUTATIONAL E NGINEERING
Problem Set 9 (due Wednesday in my mailbox by 4pm, 11/20)
Questions:
1. Wed like to solve the same problem described in the previous assignment using BtCx discretization. Heres the layout of the grid:
u1,1
u2,1
u3,1
E NGR 8103: C OMPUTATIONAL E NGINEERING
Problem Set 8 (due Friday in my mailbox by 4pm, 11/8)
Questions:
1. Find an alternative discretization for f = fxx + fyy at (a, b) using the ve points given in the
graph below (h=dx=dy). Compute the order of your di
E NGR 8103: C OMPUTATIONAL E NGINEERING
Problem Set 5 (due Friday in my mailbox by 4pm, 10/11)
Questions:
A drug is administered to a patient through injection. The drug concentration in the blood stream changes
through blood ow and diffusion according to
E NGR 8103: C OMPUTATIONAL E NGINEERING
Problem Set 3 (due Friday in my mailbox by 4pm, 09/13)
Please read the problems carefully and follow all directions. Feel free to contact me if you have any questions.
Questions:
1. The concentration of a pollutant
1. Consider the following PDE:
ut = 2 ux
(a) (2 pts.) Which discretization would you use to solve this PDE, and why? (VonNeumann analysis is not necessary to answer this question).
(b) (2 pts.) It is possible to combine transport with diusion in a single
E NGR 8103: C OMPUTATIONAL E NGINEERING
Problem Set 7 (due Friday in my mailbox by 4pm, 10/25)
Questions:
1. (3 pts.) Do the Von-Neumann Analysis for
ut = 2uxx
1
for the Crank-Nicholson scheme with s = 2 . Determine the condition for stability in terms
of
E NGR 8103: C OMPUTATIONAL E NGINEERING
Problem Set 6 (due Friday in my mailbox by 4pm, 10/18)
Questions:
Consider the simple diffusion (heat) equation:
ut = D uxx
1. Do the Von-Neumann Analysis for backward time centered space discretization to determine
E NGR 8103: C OMPUTATIONAL E NGINEERING
Problem Set 2 (due Wednesday in my mailbox by 4pm, 09/04)
Questions:
1. Provide an example (a function f (x) and a starting point x0 ) where the Newtons method fails to
converge to the root c (where f (c) = 0). Show
UNIVERSITY OF GEORGIA
ENGR 8103 - COMPUTATIONAL ENGINEERING
Fall 2012, Kazanci
Name :
Problem Score Points
1
2
3
4
5
6
Bonus
Total
7
7
4
4
7
7
7
36
100
This is a 75 minute test. No books, notes or calculators are permitted. You may use the back
of the pag