Environmental Engineering Reference
In-Depth Information
For an initial value problem with the condition
c
ðt ¼
0
Þ¼
c
0
, it can be verified
that the solution is:
C
1
f
i
c
ðtÞ¼
exp
ð
CtÞ
c
0
ð
exp
ð
CtÞ
I
Þ
(18.11)
For a zero source vector
f
i
the special solution is:
c
ðtÞ¼
exp
ð
CtÞ
c
0
(18.12)
Sidebar 18.2: MATLAB
®
Matrix Functions
Matrix functions are common functions that allow matrices as arguments.
There are several matrix functions directly implemented in MATLAB
:
®
'
fun.m'
M-file or
funm
command. How it works is best explained by an example.
Instead of using
expm (A)
as command with matrix
A
one may write:
Other matrix functions can be defined by using the MATLAB
®
In the same manner
sin, cos, sinh
or
cosh
can be called with a matrix
argument. Unfortunately, the same procedure does not work for functions
with more than one argument. Thus the call
does not work. Maas and Olsthoorn (
1997
) propose the following nice trick,
which works by introducing two new M-files:
An example for the application of (
18.11
) is given by the following command
sequence:
