Q1.
In
a general second order linear partial differential equation with two
independent variables,
![](elliptic_files/image002.gif)
where A , B , C are
functions of x and
y,
and D
is a function of
x
, y ,
, ,
then the PDE is elliptic if
B2-4AC<0
B2-4AC>0
B2-4AC=0
B2-4AC≠0
Q2.
The region in
which the following equation
![](elliptic_files/image008.gif)
acts as an
elliptic equation is
![](elliptic_files/image010.gif)
![](elliptic_files/image012.gif)
for all values of x
![](elliptic_files/image014.gif)
Q3. The
finite difference approximation of
in
the elliptic equation
![](elliptic_files/image018.gif)
at
(x,y)
can be
approximated as
![](elliptic_files/image020.gif)
![](elliptic_files/image022.gif)
![](elliptic_files/image024.gif)
![](elliptic_files/image026.gif)
Q4.
Find the
temperature at the interior node given in the following figure using the
direct method
45.19
°C
48.64
°C
50.00
°C
56.79
°C
Q5. Find
the temperature at the interior node given in the following figure
![](elliptic_files/image036.gif)
Using the
Lieberman method and relaxation factor of 1.2, the temperature at
x-=3, y=6
estimated after 2 iterations is (use the temperature of interior nodes
as 50°C
for the initial guess)
52.36
°C
53.57
°C
56.20
°C
58.64
°C
Q6.
Find the steady-state temperature at the interior node as given in the
following figure
![](elliptic_files/image038.gif)
53.57
°C
66.40
°C
68.20
°C
69.59
°C
Complete Solution
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