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ParametricNDSolveValue
ParametricNDSolveValue[eqns, expr, {t, tmin, tmax}, pars]
gives the value of expr with functions determined by a numerical solution to the ordinary differential equations eqns with the independent variable t in the range 
to 
with parameters pars.
ParametricNDSolveValue[eqns, expr, {t, tmin, tmax}, {x, xmin, xmax}]
uses a numerical solution to the partial differential equations eqns.
Details and Options
- ParametricNDSolveValue gives results in terms of ParametricFunction objects.
- A specification for the parameters pars of
can be used to specify ranges. - Possible forms for
are: -
p p has range Reals or Complexes Element[p,Reals] p has range Reals Element[p,Complexes] p has range Complexes Element[p,{v1,...}] p has discrete range 
{p,pmin,pmax} p has range 
- Typically expr will depend on the parameters indirectly, through the solution of the differential equations, but may depend explicitly on the parameters.
- Derivatives of the resulting ParametricFunction object with respect to the parameters are computed using a combination of symbolic and numerical sensitivity methods when possible.
- ParametricNDSolveValue takes the same options and settings as NDSolve.
- NDSolve and ParametricNDSolveValue typically solve differential equations by going through several different stages, depending on the type of equations. With Method->{s1->m1, s2->m2, ...}, stage
is handled by method 
. The actual stages used and their order are determined by NDSolve, based on the problem to be solved. - Possible solution stages are the same as for NDSolve, with the addition of:
-
"ParametricCaching" caching of computed solutions "ParametricSensitivity" computation of derivatives with respect to parameters
Examplesopen all
Basic Examples (3)
Get a parametric function of the parameter 
for the value of 
:
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Evaluating with a numerical value of 
gives an approximate function solution for 
:
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Plot the solutions for several different values of the parameter:
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Get a function of the parameter 
that gives the value of the function 
at 
:
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This plots the value as a function of the parameter a:
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Use the function with FindRoot to find a root:
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Show the sensitivity of the solution of a differential equation to parameters:
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The sensitivity with respect to a increases with t:
| In[2]:= |
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The sensitivity with respect to 
does not increase with t:
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