https://github.com/makramkd/numerical-integration
A set of numerical integration routines in C++.
https://github.com/makramkd/numerical-integration
Last synced: 3 months ago
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A set of numerical integration routines in C++.
- Host: GitHub
- URL: https://github.com/makramkd/numerical-integration
- Owner: makramkd
- License: mit
- Created: 2015-12-09T15:39:02.000Z (over 9 years ago)
- Default Branch: master
- Last Pushed: 2015-12-11T03:55:57.000Z (over 9 years ago)
- Last Synced: 2023-03-01T16:22:15.199Z (about 2 years ago)
- Language: C++
- Size: 36.1 KB
- Stars: 1
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# numerical-integration
A set of numerical integration routines in C++.
# The details
We will implement the following routines/algorithms for numerical integration:
- Rectangle rule : this is as stupid as it gets
- Trapezoidal rule : just a bit smarter than rectangle rule.
- Iterated rule: break up the interval [a,b] into smaller pieces and use the rectangle or trapezoidal rule on these pieces,
then add up these separate sums (this kind of looks like Riemann sums)
- Simpson's rule: a numerical approximation to the definite integral credited to Thomas Simpson, a mathematician from the
1700s. It involves approximating the integrable function `f` by a polynomial `P` and then integrating that polynomial.
- Adaptive quadrature: you integrate `f` over some interval, and you check the error with the real value of the integral.
If it's too large, you integrate again, but over two different intervals, and with a smaller tolerance.