April 2016
Intermediate to advanced
886 pages
26h 47m
English
Content preview from Electromagnetic Waves, Materials, and Computation with MATLAB®
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738 Appendix 16E: Numerical Techniques intheSolution of Field Problems
If the error criterion specied is that there should not be any change up to A places of a
value and if the guessed value
V
j k,
0
is zero, then n
c
the number of iterations required may
be calculated as follows:
K
X X X
X X X X X X X
A
n
P Q R
A B C D
c
j k
n
j k
c
*
.
.
(
,
,
= =
ε
ε
zeros
0
000 0
1 2 3
… …
… …
iis in the numerator).
Taking log
10
on both sides,
n K A
n
A
K
c
c
,log * ( ) ( )
log *
.
10
10
1 1≈ + − −
≈
−
Thus, for the Richardson method,
n
A
M N
A
M N
c
=
− +
( )
⎡
⎣
⎢
⎤
⎦
⎥
≈
− − +
⎡
⎣
⎤
⎦
log cos cos log ( ) ( )
10 10
2 2
1
2
1
1
4
π π π π
⎛⎛
⎝
⎜
⎞
⎠
⎟
.
(16E.13)
For Liebman and extrapolated Liebman method
On the same lines as for ...
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