Home Login  |   Contact  |   About Us       Tuesday, May 17, 2022   

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



Skip Navigation Links.



"Numerical Integration Solutions"
Gauss-Chebyshev Method

N RESULT 


(Actually after 2 is a repetition)


Results from the 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


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.
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
KMP ARTICLES
Brand





Home

Login

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