#rectanglemethod — Public Fediverse posts

The trapezium rule is quite an improvement to the above and each area is approximated by joining up the ordinates at the beginning and end of each discrete interval with a straight line. This converges appreciably faster than the above method.

#MyWork #Mathematics #Maths #Numerics #RectangleMethod #TrapeziumRule #SimpsonsRule #FreeSoftware #CCBYSA #Wikipedia #Wikimedia

The rectangle method is the most simple-minded and crudest method of finding the area below the curve. It converges slowly.

#MyWork #Mathematics #Maths #Numerics #RectangleMethod #TrapeziumRule #SimpsonsRule #FreeSoftware #CCBYSA #Wikipedia #Wikimedia

Literally a couple of years ago I posted some #AnimatedGifs of the simplest #NumericalIntegration techniques, namely the #RectangleMethod, the #TrapeziumRule and #SimpsonsRule. In the comments, somebody suggested that I show the errors of each method as the number of strips increases. I said I’d try to do it when I got time. In principle it is a simple but worthwhile request but getting a bit of time and motivation to do it is another matter. Also, I needed a way to change labels dynamically...

Here are #animated #gifs of the representation of #NumericalIntergration #approximations with increasing numbers of strips. Represented are the Rectangle Method, Trapezium Rule and Simpson’s Rule. Note how much faster the second and third methods improve the approximation the exact blue curve in each case as the number of strips increases. Produced using #wxmaxima. They are all available on #Wikipedia.

#MyWork #Mathematics #Maths #Numerics #RectangleMethod #TrapeziumRule #SimpsonsRule #CCBYSA