SYM Paclet Symbol
EulerOperator
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SYM Overview
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HomotopyOperator
HomotopyOperator[
fun
][
expr
]
gives the result of the action of the Homotopy operator on an expression
expr
with respect to a set of functions,
fun
.
MORE INFORMATION
To use
HomotopyOperator
, you first need to load the
SYM Package
using
Needs
["SYM`"].
fun
is the list of functions.
expr
can be any expression including the functions and the derivatives of them.
EXAMPLES
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Basic Examples
(2)
In[1]:=
Let the expression between the two functions
u,
:
In[2]:=
Out[2]=
In[3]:=
Out[3]=
When the Euler Operator is 0 a vector function can be found that its divergence gives back the expression using the Homotopy operator. For the one dimensional case this is equivalent to integrating the function:
In[4]:=
Out[4]=
Indeed,
In[5]:=
Out[5]=
In[1]:=
Let the expression:
In[2]:=
Out[2]=
In[3]:=
Out[3]=
Again, a vector function can be obtained via the Homotopy operator
In[4]:=
Out[4]=
Indeed,
In[5]:=
Out[5]=
SEE ALSO
EulerOperator
MORE ABOUT
SYM Overview