Client Account:   Login
Home Site Statistics   Contact   About Us   Sunday, March 26, 2017

users on-line: 2 | Forum entries: 6   
j0185201- Back to Home
   Skip Navigation LinksHOME › AREAS OF EXPERTISE › Numerical Integration in Smalltalk     › ~ Simpson Method


      Skip Navigation Links
   SIMPSON METHOD   
   IMPLEMENTATION   
   OUR SOLUTIONS   
 

METHODS
Simpson Method

The Simpson approach states that the "integration range [a,b]" can always be divided into n (n must be even) strips of width h = (b - a) / n. Applying the Simpson's rule to two adjacent strips:

xi+2xi f(x)dx = h/3 [f(xi) + 4 f(x(i+1) + f(xi+2)]

Then the integral can be obtained by the sum:

I = ba f(x)dx =
ni=0,2,4,... x i+2xi f(x)dx =
h/3 ∑ ni=0,2,4,... [f(xi>) + 4 f(xi+1) + f(xi+2)]

It must also be stated that the Simpson's 1/3 rule requires the number of strips n to be even. If this condition is not satisfied, it is posible to integrate over the first (or last) three strips by using Simpson's 3/8 rule (which is another condition):

I = 3h/8 [f(x0) + 3 f(x1) + 3 f(x2) + f (x3)]

and then use the Simpson's 1/3 rule for the rest of strips. Although a bit confusing it is really very simple to implement this rule.





Skip Navigation Links.

Home Skip Navigation Links
   Algorithms, Graphics, Vectors,
            implementation techniques.
   Mineral Transactions info,
            sales, agreements...
   Numerical Modeling services
            mineral environment.
   Want to know about Mining?
            basic knowledge here...
   What are Mineral Commodities?
            our elementary charts.
   Math, Analysis and More...
            our expertise in the matter.

 

Platform Implementation

Home Algorithm Implementation
We design applications for different environments and platforms...
        Home Graphics and Animation
The graphics classes in Smalltalk were designed...
        Home Optimization Algorithms
An optimization problem is a numerical problem...
        Home Vectors and Matrices
The concise notation introduced in linear algebra for vector...
 



2017 © Keystone Mining Post  |   2461 E. Orangethorpe Av., Fullerton, CA 92631 USA  |   info@keystoneminingpost.com