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2.10 Nonlinear Symbolic Approximation 175
DT analysis mode for error checking, specifying sweep ranges for both input values VLOAD and II.
NonlinearSetup performs a numerical reference simulation and stores the result in the returned
DAEObject. These numerical values are used automatically to calculate the error in subsequent
simplification steps.
In[20]:= step2 = NonlinearSetup[step1, {II, VLOAD}, {I$VLOAD},
DT −> {Range −>
{{VLOAD, 0., 3.5, 0.5}, {II, 0., 0.001, 0.0002}} }]
Out[20]= DAEDC, 6 6
Cancelling Terms
Once we have set up the DAE system we call CancelTerms (Section 3.12.3) where we specify an
error bound for the output variable. CancelTerms then deletes terms in the equation system using
this error bound. Afterwards we again use Statistics to inspect the complexity reduction achieved
by CancelTerms.
In[21]:= step3 = CancelTerms[step2, {DT −> {I$VLOAD −> 25.*^−6}}]
Out[21]= DAEDC, 6 6
In[22]:= Statistics[step3]
Number of equations : 6
Number of variables : 6
Length of equations : {2, 2, 2, 4, 2, 1}
Terms with derivatives : 0
Sums in levels : {12, 4}
Note that CancelTerms reduces the number of terms drastically.
Compressing Equations again
Deletion of terms changes the equations in such a way that it is often possible to further solve
equations for some variables. Thus, we can again try to eliminate variables using
CompressNonlinearEquations. Here, two more equations can be removed from the system. Note
that CompressNonlinearEquations automatically retrieves the settings made by NonlinearSetup,
so there is no need to specify the variable of interest I$VLOAD as a second argument. Afterwards we
drop those parameters from the design point which no longer appear in the equation system using
UpdateDesignPoint (Section 3.6.14).
In[23]:= step4 = CompressNonlinearEquations[step3]
Out[23]= DAEDC, 4 4