1
Sep. 12, 2006
ATMS 502  CS 505  CSE 566
Jewett
Computer Problem 2
2 and 3timelevel multimethod comparison and evaluation
Due
: beginning of class – Thursday, Sep. 28.
Turn in
: your code (printed out, and
also
emailed to me), and plotted results (on paper).
Problem being solved:
linear advection equation.
Boundary condition:
periodic; c>0.
Evaluation:
you will overlay the true solution with each of your numerical results,
as well as compute error statistics following Takacs (1985, eqn. 6.16.7).
Schemes:
there are three:
1. LaxWendroff
(from
computer problem 1)
u
j
n
+
1
=
u
j
n
"
#
2
u
j
+
1
n
"
u
j
"
1
n
(
)
+
$
u
j
+
1
n
"
2
u
j
n
+
u
j
"
1
n
(
)
2. Takacs (1985, eqn. 4.3)
u
j
n
+
1
=
u
j
n
"
#
2
u
j
+
1
n
"
u
j
"
1
n
(
)
+
#
2
2
u
j
+
1
n
"
2
u
j
n
+
u
j
"
1
n
(
)
"
$# #
"
1
(
)
u
j
+
1
n
"
3
u
j
n
+
3
u
j
"
1
n
"
u
j
"
2
n
(
)
3. Leapfrog (3timelevel)
u
j
n
+
1
=
u
j
n
"
1
"
#
u
j
+
1
n
"
u
j
"
1
n
(
)
(no Asselin filtering)
Note the additional boundary term (j2) above; you will have to change your array dimensions.
For all of the above,
"
=
c
#
t
#
x
,
and
$
=
1
+
"
6
; all problems are linear.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 JEWETT
 Numerical Analysis, Takacs, Boundary value problem, Pearson productmoment correlation coefficient, true solution

Click to edit the document details