Home Site Statistics  |   Contact  |   About Us       Wednesday, April 01, 2020   

j0182018 - Back to Home
   Skip Navigation LinksHOME › AREAS OF EXPERTISE › Numerical Integration     › ~ Gauss-Chebyshev Method


"Numerical Integration Solutions"
Gauss-Chebyshev Method

N RESULT 


(Actually after 2 is a repetition)

Results from Gauss-Chebyshev method



IMPLEMENTATION
Gauss-Chebyshev Integration

To compute the following Gaussian integral using the Gauss-Chebyshev method:

I = ∫-11 (1 - x2) 3/2 dx

The delegate function is simply (1 - x2)2, since the weighting function w(x) = 1 / √1 - x2 for the Gauss-Chebyshev integration.

Running this example creates the results shown above. The exact result of this integral is equal to 3π / 8. The result for n = 2 already gives the exact result, which is expected because the function (1 - x2)2 is a polynomial of degree four, meaning the Gauss-Chebyshev integration is exact with three nodes.



Testing the Gauss-Chebyshev Integration Method

In order to test the Gauss-Hermite method as defined above, a new TestGaussHermite() static method has been added and executed. Supporting code and methods are not shown.

           static void TestGaussChebyshev();
              {
                 ListBox1.Items.Clear();
                 ListBox2.Items.Clear();
                 double result;
                 for (int n = 1; n < t1; n++)
                 (
                   result = Integration.GaussChebyshev(f5, n);
                   ListBox1.Items.Add(" " + n + );
                   ListBox2.Items.Add(" " + result);
                 )
              }



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
Function Evaluation


You are viewing this tab ↓
Skip Navigation Links.



Consulting Services - Back to Home
Home

Home Math, Analysis,
  expertise..."

EIGENVALUE SOLUTIONS...
Eigen Inverse Iteration
Rayleigh-Quotient Method
Cubic Spline Method

 

Applied Mathematical Algorithms

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

Complex Functions
Home Non-linear system methods...

Non Linear Systems
Home Construction of differentiation...

Differentiation
Home Consider the function where...

Integration
 
About Us

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

KMP Website >
Site Statistics >
Contact Us

KMP ENGINEERING
2461 E Orangethorpe Ave Fullerton, CA 92631 USA info@keystoneminingpost.com
Site Map

> Home
> Areas of Expertise
> Reference Items
> Managed Services
> Login

Mining & Software Engineering

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