Home Site Statistics  |   Contact  |   About Us       Sunday, February 16, 2020   

j0182018 - Back to Home
   Skip Navigation LinksHOME › AREAS OF EXPERTISE › Numerical Integration     › ~ Variance: Trapeze,Simpson,Romberg

      Skip Navigation Links

Integration of Functions

Regarding Integration of Functions...

Many functions are defined by an integral.

Integrals are useful in probability theory to compute the probability of obtaining a value over a given interval.

Integrals come up in the computation of surfaces and of many physical quantities related to mechanics, energy, power and others and finally numerical integrals are accurate procedures that formally consist of an infinite sum of infinitesimal quantities.

We have already introduced the use of (see menu under)  "Simpson Method " in a real world application.

We want to show how different methods offer strategies that deal with number of iterations, estimated precision of the results and absolute values of the difference between the result of the integration and the true result. This time we implemented under the Smalltalk environment.

We chose three methods of integration approximation: Trapeze, Simpson and Romberg to illustrate progress of function evaluation in each situation. The function to integrate:

f(x) = 1 / x

is specified as a block closure to be implemented in Smalltalk:

f := [:x | 1 / x]

You are viewing this tab ↓
Skip Navigation Links.

Consulting Services - Back to Home

Home Math, Analysis & More,
  established expertise..."

Eigen Inverse Iteration
Rayleigh-Quotient Method

Cubic Spline Method
Newton Divided Difference


Applied Mathematical Algorithms

     Home Complex Functions
A complex number z = x + iy, where...

Complex Functions
     Home Non-Linear Systems
Non-linear system methods...

Non Linear Systems
     Home Differentiation
Construction of differentiation...

     Home Integration
Consider the function where...

  KMP Engineering  
 Location: 2461 E Orangethorpe Ave. 
 Fullerton, CA 92631 USA Email:info@keystoneminingpost.com

Since 2006 All rights reserved © KMP Engineering