class |
AdaptiveCompositeIntegrator1D |
Adaptive composite integrator: step size is set to be small if functional variation of integrand is large
The integrator in individual intervals (base integrator) should be specified by constructor.
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class |
ExtendedTrapezoidIntegrator1D |
The trapezoid integration rule is a two-point Newton-Cotes formula that
approximates the area under the curve as a trapezoid.
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class |
GaussHermiteQuadratureIntegrator1D |
Gauss-Hermite quadrature approximates the value of integrals of the form
$$
\begin{align*}
\int_{-\infty}^{\infty} e^{-x^2} g(x) dx
\end{align*}
$$
The weights and abscissas are generated by GaussHermiteWeightAndAbscissaFunction. |
class |
GaussianQuadratureIntegrator1D |
Class that performs integration using Gaussian quadrature.
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class |
GaussJacobiQuadratureIntegrator1D |
Gauss-Jacobi quadrature approximates the value of integrals of the form
$$
\begin{align*}
\int_{-1}^{1} (1 - x)^\alpha (1 + x)^\beta f(x) dx
\end{align*}
$$
The weights and abscissas are generated by GaussJacobiWeightAndAbscissaFunction. |
class |
GaussLaguerreQuadratureIntegrator1D |
Gauss-Laguerre quadrature approximates the value of integrals of the form
$$
\begin{align*}
\int_{0}^{\infty} e^{-x}f(x) dx
\end{align*}
$$
The weights and abscissas are generated by GaussLaguerreWeightAndAbscissaFunction. |
class |
GaussLegendreQuadratureIntegrator1D |
Gauss-Legendre quadrature approximates the value of integrals of the form
$$
\begin{align*}
\int_{-1}^{1} f(x) dx
\end{align*}
$$
The weights and abscissas are generated by GaussLegendreWeightAndAbscissaFunction. |
class |
RombergIntegrator1D |
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class |
RungeKuttaIntegrator1D |
Adapted from the forth-order Runge-Kutta method for solving ODE.
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class |
SimpsonIntegrator1D |
Simpson's integration rule is a Newton-Cotes formula that approximates the
function to be integrated with quadratic polynomials before performing the
integration.
|