Modifier and Type | Interface and Description |
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interface |
IterativeIntegrator
An iterative integrator computes an integral by a series of sums, which approximates the value of the integral.
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Modifier and Type | Class and Description |
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class |
ChangeOfVariable
Change of variable can easy the computation of some integrals, such as improper integrals.
|
class |
Riemann
This is a wrapper class that integrates a function by using an appropriate integrator together with Romberg's method.
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Constructor and Description |
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ChangeOfVariable(SubstitutionRule change,
Integrator integrator)
Construct an integrator that uses change of variable to do integration.
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Modifier and Type | Class and Description |
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class |
GaussChebyshevQuadrature
Gauss-Chebyshev Quadrature uses the following weighting function:
\[
w(x) = \frac{1}{\sqrt{1 - x^2}}
\]
to evaluate integrals in the interval (-1, 1).
|
class |
GaussHermiteQuadrature
Gauss-Hermite quadrature exploits the fact that quadrature approximations are open integration
formulas (that is, the values of the endpoints are not required) to evaluate of integrals in the
range \((-\infty, \infty )\).
|
class |
GaussianQuadrature
A quadrature rule is a method of numerical integration in which we approximate the integral of a
function by a weighted sum of sample points.
|
class |
GaussLaguerreQuadrature
Gauss-Laguerre quadrature exploits the fact that quadrature approximations are open integration
formulas (i.e.
|
class |
GaussLegendreQuadrature
Gauss-Legendre quadrature considers the simplest case of uniform weighting: \(w(x) = 1\).
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Modifier and Type | Class and Description |
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class |
Midpoint
The midpoint rule computes an approximation to a definite integral,
made by finding the area of a collection of rectangles whose heights are determined by the values of the function.
|
class |
NewtonCotes
The Newton-Cotes formulae, also called the Newton-Cotes quadrature rules or simply Newton-Cotes rules,
are a group of formulae for numerical integration (also called quadrature) based on evaluating the integrand at equally-spaced points.
|
class |
Romberg
Romberg's method computes an integral by generating a sequence of estimations of the integral value and then doing an extrapolation.
|
class |
Simpson
Simpson's rule can be thought of as a special case of Romberg's method.
|
class |
Trapezoidal
The Trapezoidal rule is a closed type Newton-Cotes formula, where the integral interval is evenly divided into N sub-intervals.
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