ParametricFunction

represents a function that computes a solution when evaluated with numerical values for the parameters pars.

Details

ParametricFunction is generated by ParametricNDSolve and ParametricNDSolveValue.
A ParametricFunction object pfun is evaluated by using pfun[pvals] where pvals are explicit numerical values for the parameters pars.
A ParametricFunction may return numbers, functions, or more complicated expressions based on the underlying computation.
Derivatives of ParametricFunction are computed using a combination of symbolic and numerical sensitivity methods when possible.

Examples

Parameters for a harmonic oscillator:

Wolfram Language code: pfun = ParametricNDSolveValue[ {x''[t] + γ x'[t] + ω^2x[t] == 0, x[0] == 1, x'[0] == 0}, x, {t, 0, 10}, {γ, ω}]

With numerical values, an approximate function is returned:

Wolfram Language code: xsol = pfun[.1, 4]

Wolfram Language code: Plot[xsol[t], {t, 0, 10}]

Derivatives of the ParametricFunction give the sensitivity solutions:

Wolfram Language code: Plot[Evaluate[D[pfun[γ, ω][t], γ] /. {γ -> .1, ω -> 4}], {t, 0, 10}]

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