1.5 Domain Solution
On solution of the integral
equation (approximations to)
the unknown boundary function(s) will be known on S.
Hence both of f(q) and
¶f(q)/ ¶nq will be explicit if the method
is based on the integral equation (5).
In most cases a solution in the domain D is required and this
can be found using the following equation
|
f(p) = |
ó
õ
|
S
|
G(p,q) |
¶f
¶nq
|
dSq - |
ó
õ
|
S
|
|
¶G
¶nq
|
(p,q) f(q) dSq (p Î D) |
| (6) |
or, more concisely,
|
f(p) = { L f}S -{ M v }S (p Î D) , |
|
using the notation of Section 1.3.
The equation (6) is also an outcome of
Green's second theorem. The domain solution f(p)
for any point p in the domain can be obtained
through simply evaluating the integrals in (6).
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