Namespaces

Types in MathNet.Numerics

Type DifferIntegrate

Namespace MathNet.Numerics

Static Functions

Public Static Functions

double DoubleExponential(Func<double, double> f, double x, double order, double x0, double targetAbsoluteError)

Evaluates the Riemann-Liouville fractional derivative that uses the double exponential integration.

order = 1.0 : normal derivative

order = 0.5 : semi-derivative

order = -0.5 : semi-integral

order = -1.0 : normal integral

Parameters
Func<double, double> f

The analytic smooth function to differintegrate.

double x

The evaluation point.

double order

The order of fractional derivative.

double x0

The reference point of integration.

double targetAbsoluteError

The expected relative accuracy of the Double-Exponential integration.

Return
double

Approximation of the differintegral of order n at x.

double GaussKronrod(Func<double, double> f, double x, double order, double x0, double targetRelativeError, int gaussKronrodPoints)

Evaluates the Riemann-Liouville fractional derivative that uses the Gauss-Kronrod integration.

order = 1.0 : normal derivative

order = 0.5 : semi-derivative

order = -0.5 : semi-integral

order = -1.0 : normal integral

Parameters
Func<double, double> f

The analytic smooth function to differintegrate.

double x

The evaluation point.

double order

The order of fractional derivative.

double x0

The reference point of integration.

double targetRelativeError

The expected relative accuracy of the Gauss-Kronrod integration.

int gaussKronrodPoints

The number of Gauss-Kronrod points. Pre-computed for 15, 21, 31, 41, 51 and 61 points.

Return
double

Approximation of the differintegral of order n at x.

double GaussLegendre(Func<double, double> f, double x, double order, double x0, int gaussLegendrePoints)

Evaluates the Riemann-Liouville fractional derivative that uses the Gauss-Legendre integration.

order = 1.0 : normal derivative

order = 0.5 : semi-derivative

order = -0.5 : semi-integral

order = -1.0 : normal integral

Parameters
Func<double, double> f

The analytic smooth function to differintegrate.

double x

The evaluation point.

double order

The order of fractional derivative.

double x0

The reference point of integration.

int gaussLegendrePoints

The number of Gauss-Legendre points.

Return
double

Approximation of the differintegral of order n at x.