Multiple-Choice Test
Chapter 10.02
Parabolic Partial Differential Equations
1.
In a general second order linear partial differential equation with two independent
variables
 2u
 2u
 2u
A 2 B
C 2  D  0
xy
x
y
u u
where A , B , C are functions of x and y , and D is a function of x , y ,
,
,
x y
then the partial differential equation is parabolic if
(A) B 2  4 AC  0
(B) B 2  4 AC  0
(C) B 2  4 AC  0
(D) B 2  4 AC  0
2.
The region in which the following partial differential equation
2
 2u
 2u
3  u
x
 27 2  3
 5u  0
xy
x 2
y
acts as parabolic equation is
(A)
1
x 
 12 
1/ 3
1/ 3
1
(B) x   
 12 
(C) for all values of x
(D)
3.
1
x 
 12 
1/ 3
10.02.1
The partial differential equation of the temperature in a long thin rod is given by
T
 2T
 2
t
x
10.03.2
Chapter 10.03
node  0
1
2
3
T  80 C
T  20 C
9 cm
If   0.8 cm 2 / s , the initial temperature of rod is 40 C , and the rod is divided into
three equal segments, the temperature at node 1 (using t  0.1 s ) by using an explicit
solution at t  0.2 sec is
(A) 40.7134 0 C
(B) 40.6882 0 C
(C) 40.7033 0 C
(D) 40.6956 0 C
4.
The partial differential equation of the temperature in a long thin rod is given by
T
 2T
 2
t
x
node  0
1
2
T  80 C
3
T  20 C
9 cm
If   0.8 cm 2 / s , the initial temperature of rod is 40 C , and the rod is divided into
three equal segments, the temperature at node 1 (using t  0.1 s ) by using an
implicit solution for t  0.2 sec is
(A) 40.7134 0 C
(B) 40.6882 0 C
(C) 40.7033 0 C
(D) 40.6956 0 C
10.03.2
10.06.3
5.
Chapter 10.06
The partial differential equation of the temperature in a long thin rod is given by
T
 2T
 2
t
x
node  0
1
3
2
T  80 C
T  20 C
9 cm
If   0.8 cm 2 / s , the initial temperature of rod is 40 C , and the rod is divided into
three equal segments, the temperature at node 1 (using t  0.1 s ) by using a CrankNicolson solution for t  0.2 sec is
(A) 40.7134 0 C
(B) 40.6882 0 C
(C) 40.7033 0 C
(D) 40.6956 0 C
6.
The partial differential equation of the temperature in a long thin rod is given by
T
 2T
 2
t
x
node  0
1
2
3
T  20 C
insulated
9 cm
If   0.8 cm 2 / s , the initial temperature of rod is 40 C , and the rod is divided into
three equal segments, the temperature at node 1 (using t  0.1 s ) by using an explicit
solution at t  0.2 sec is
10.03.4
Chapter 10.03
T
 h(Ta  T0 ) ), where k  9 W /( m C ) , h  20W / m 2 , Ta  25 C ,
x
and T0  (the temperature of rod at node 0)
(For node 0, k
(A)
(B)
(C)
(D)
10.03.2
41.6478 0 C
38.4356 0 C
39.9983 0 C
37.5798 0 C