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WOLFRAM|DEMONSTRATIONS PROJECT

Green's Function

​
order
1
2
3
4
sign
positive
negative
m
0.1
boundary conditions
periodic
initial
final
This Demonstration shows the graphic of the Green's function
G(t,s)
related to the linear differential equation of order
n=1
,
n=2
,
n=3
, or
n=4
,
(n)
u
(s)+a
n
m
u(s)=σ(s)
,
where
a=±1
and with the following linear boundary conditions:
n=1
: periodic:
u(0)=u(1)
, initial:
u(0)=0
, or final:
u(1)=0
;
n=2
: periodic:
u(0)=u(1),u'(0)=u'(1)
, Dirichlet:
u(0)=u(1)=0
or Neumann:
u'(0)=u'(1)=0
;
n=3
: periodic:
u(0)=u(1),u'(0)=u'(1),u''(0)=u''(1)
;
n=4
: periodic:
u(0)=u(1),u'(0)=u'(1),u''(0)=u''(1),u'''(0)=u'''(1)
, simply supported beam:
u(0)=u(1)=u''(0)=u''(1)=0
, or clamped beam
u(0)=u(1)=u'(0)=u'(1)=0
.
The solution of the boundary value problem (differential equation and boundary conditions) is given by
u(t)=
1
∫
0
G(t,s)σ(s)ds
.
In the code, the expression for the corresponding Green's function is given for an arbitrary interval
[a,b]
.
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