{ Numerical Methods}

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Permission to use, copy, and distribute this software and It’s documentation for any non commercial purpose is hereby granted without fee, provided: THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL Henrik Vestermark, BE LIABLE FOR ANY SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.


Numerical Integration:


Integration & Graphing vs. 1.9
 
Verbose
Integration Method
Trapez Simpson Romberg Fox-Romberg
Gauss-Legendre Gauss-Chebyshev Gauss-Hermite Double Exponential
     
 
Display Options
Xmin: Xmax: Ymin: Ymax:
  • Results
  • Graphing
  • Convergence
  • Delta-E
  • Help

Graphing

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Convergence

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Delta-E

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Help

Explanation: Enter the equation that needs to be displayed. The usual math function can be used: +.-.*,/,(,), abs(), acos(), asin(), atan(), atan2(), cos(), exp(), log(), pow(), sin(), sqrt(), tan(). Note for x^3 used the pow(x,3) notation and log() is the natural logarithm
If you need integration as well, checkmark on one or more integration methods. For fastest and most accurate method use Fox-Romberg, Double exponential or Gauss.
For accuracy the methods takes it to the numeric limits, however to avoid time consuming operations the limits on number function evaluation is around 65536 calls.
Note: Gauss-Chebyshev required that the function is on the form f(x)/sqrt(1-x^2) otherwise result are incorrect. Gauss-Hermite required that the function is on the form e-x^2*f(x).
The Test button setup a default equation (for testing only). Note that the interval [0,0.5] contains a singularity for x=0 making it hard for Trapez, Simpson and Romberg method to get a high accuracy on the result. Fox-Romberg can handle this to the numeric limit!
Email: hve@hvks.com if you have any questions.
This version has been tested with both IE8, Chrome, FireFox 3 & Safari browser.
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Corrections:
25-Nov-2011 vs 1.8 Layout changes and switching to using canvas object for HTML graphic. Now Print also print the Graphic of the Function, Convergence Power and Delta-E values
28-May-2011 vs 1.7 Fixed an issue with prematurely stop of the integration resulting in wrong result. This was demonstrated with f(x)=x-floor(x) in [0,6.4]
04-May-2011 vs 1.6 Added Email and rearranged the layout
15-Nov-2009 vs 1.5 Added Double Expoential integration method
21-May-2007 vs 1.4 Added Gauss-Hermite integration
17-May-2007 vs 1.3 Added Gauss-Chebyshev integration and more display options
09-May-2007 vs 1.2 Added Gauss-Legendre integration method
23-Apr-2007: vs 1.1 Initial release
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