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Mathematics Calculus Wolfram Language Numerical Computation

Speed up Nintegrate for certain range of function's input

John Wick

Posted 2 years ago

POSTED BY: John Wick

6 Replies

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 2 years ago

When integrating, I would recommend `UnitStep` instead of `HeavisideTheta`. This gives me a symbolic output: With[{g = 10^-23, c = 10^14}, Integrate[ Simplify[(6 (10^-10 Sqrt[ xP])^2 10^-11 (10^-7 Sqrt[(10^-38 c^2 xP + (10^-10 Sqrt[ xP])/x)/(1/10 + 10^-38 c^2)])^3)/((10^-38 c^2 xP + (10^-10 Sqrt[xP])/ x)^4/(1/10 + 10^-38 c^2)^4)* UnitStep[10^-38 c^2 xP + (10^-10 Sqrt[xP])/x - 1/g]], {xP, 1/g, 10^12}, Assumptions -> And[c > 0, x > 0, xP > 0, g > 0]]]

When integrating, I would recommend UnitStep instead of HeavisideTheta. This gives me a symbolic output:

With[{g = 10^-23, c = 10^14}, 
 Integrate[
  Simplify[(6 (10^-10 Sqrt[
           xP])^2 10^-11 (10^-7 Sqrt[(10^-38 c^2 xP + (10^-10 Sqrt[
                  xP])/x)/(1/10 + 
              10^-38 c^2)])^3)/((10^-38 c^2 xP + (10^-10 Sqrt[xP])/
           x)^4/(1/10 + 10^-38 c^2)^4)*
    UnitStep[10^-38 c^2 xP + (10^-10 Sqrt[xP])/x - 1/g]],
  {xP, 1/g, 10^12},
  Assumptions -> And[c > 0, x > 0, xP > 0, g > 0]]]

POSTED BY: Gianluca Gorni

John Wick

Posted 2 years ago

But I can't assume `{g = 10^-23, c = 10^14}` as a general solution since it will give the results for a point but in principle `g,c` have to vary for a range of values `g=>(10^-2,10^-24)` and `c=>(10^10-10^15)`

POSTED BY: John Wick

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 2 years ago

If Mathematica doesn't do it automatically, you can easily work out the point where the `HeavisideTheta` discontinuity lies, and the conditions under which that point is to the left, within, or to the right of the integration interval `[1/g, 10^12]`.