https://github.com/vovandreevik/quanc8-fmin-zeroin

The program calculates the luminosity of a blackbody using the QUANC8 algorithm and explores the sustainability of solutions in a given mathematical context.
https://github.com/vovandreevik/quanc8-fmin-zeroin

blackbody cpp fmin luminosity minimization quanc8 zeroin

Last synced: 3 days ago
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The program calculates the luminosity of a blackbody using the QUANC8 algorithm and explores the sustainability of solutions in a given mathematical context.

• Host: GitHub
• URL: https://github.com/vovandreevik/quanc8-fmin-zeroin
• Owner: vovandreevik
• Created: 2024-04-05T08:08:08.000Z (9 months ago)
• Default Branch: main
• Last Pushed: 2024-04-05T09:11:46.000Z (9 months ago)
• Last Synced: 2024-11-02T21:03:50.591Z (about 2 months ago)
• Topics: blackbody, cpp, fmin, luminosity, minimization, quanc8, zeroin
• Language: C++
• Homepage:
• Size: 17.6 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# QUANC8-FMIN-ZEROIN

The program calculates the luminosity of a blackbody and explores the sustainability of solutions in the temperature range from $T = 1000°K$ to $T = 9000°K$ in increments of $T = 1000°K$

Using the FMIN program, the program calculates the value of $z^*$ by minimizing the function $f(z)=e^z (2z^2-4)+ (2z^2-1)^2+ e^2z- 3z^4$ in the interval $[-2,-1]$.

Multiplying $z^*$ by $(-3.039830×10^{-5})$ and getting $λ_1$ (the lower limit of integration).

Using the ZEROIN program, the program calculates the $y^*$ root of the equation: $2\sqrt{x}=cos \displaystyle\frac{πx}{2}$

Multiplying $y^*$ by $(31.66675×10^{-5})$ and getting $λ_2$ (the upper limit of integration).

Using the QUANC8 program, the luminosity is calculated (as a percentage) using the formula $EFF= \displaystyle\frac{64.77}{T^4}\int_{λ_1}^{λ_2} \displaystyle\frac{\mathrm{d}x}{x^5(e^{\displaystyle\frac{1.432}{Tx}} - 1)}$ in the temperature range from $T = 1000°K$ to $T = 9000°K$ in increments of $1000°$K.

The impact of errors in changing $λ_1$ and $λ_2$ on accuracy has been evaluated.

_`quanc8.h` and `Forsythe.h` are library programs_