Home Login  |   Contact  |   About Us       Tuesday, March 19, 2024   

j0182018 - Back to Home
   Skip Navigation LinksHOME ›  AREAS OF EXPERTISE  #3 ›   Numerical Integration ›  ~ Simpson Method



Skip Navigation Links.




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.



Other Implementations...


Object-Oriented Implementation
Graphics and Animation
Sample Applications
Ore Extraction Optimization
Vectors and Matrices
Complex Numbers and Functions
Ordinary Differential Equations - Euler Method
Ordinary Differential Equations 2nd-Order Runge-Kutta
Ordinary Differential Equations 4th-Order Runge-Kutta
Higher Order Differential Equations
Nonlinear Systems
Numerical Integration
Numerical Differentiation







   Quotes

Consulting Services - Back to Home


Home

Home Math, Analysis,
  expertise..."

EIGENVALUE
SOLUTIONS...


> Rayleigh-Quotient Method

> Cubic Spline Method

 

Applied Mathematical Algorithms

Home

ComplexFunctions

Home

NonLinear
Home

Differentiation
Home

Integration
About Us


KMP Software Engineering is an independent multidisciplinary engineering consulting company specializing in mathematical algorithms.

      (About Us) →
Areas of
Expertise


SpecialFunctions
VectorsMatrices
OptimizationMethods
ComplexNumbers
Interpolation
CurveFitting
NonLinearSystems
LinearEquations
DistributionFunctions
NumericalDifferentiation
NumericalIntegration
DifferentialEquations
Smalltalk
FiniteBoundary
Eigenvalue
Graphics
Understanding
Mining


MiningMastery
MineralNews
MineralCommodities
MineralForum
Crystallography
Services


NumericalModeling
WebServices
MainframeServices
OutsourceServices

LINKED IN
MINE REVIEW(by G.Pacheco)
Brand





Home

Login

Contact
Since 2006 All Rights Reserved  © KMP Software Engineering LINKS | PRIVACY POLICY | LEGAL NOTICE