Module numerical_methods_ext 

Extended numerical methods: integral equations, BEM, radial basis functions.

Provides high-order quadrature, spline interpolation, RBF interpolation, barycentric interpolation, and Richardson-extrapolated differentiation.

Structs

BarycentricInterpolation

Barycentric interpolation (Berrut second form).

GaussHermiteQuad

Gauss-Hermite quadrature for ∫f(x)e^{-x²}dx on (-∞, +∞).

GaussKronrod

Gauss-Kronrod G7K15 adaptive quadrature.

GaussLegendreQuad

Gauss-Legendre quadrature rule with n nodes on [-1, 1].

NumericalDifferentiation

Richardson-extrapolated numerical differentiation.

RadialBasisFunction

Radial basis function interpolation in arbitrary dimension.

RombergIntegration

Romberg integration using Richardson extrapolation table.

SimpsonRule

Adaptive Simpson’s rule (1/3 rule).

SplineInterpolation

Natural cubic spline interpolation.

TrapezoidalRule

Adaptive trapezoidal rule with Richardson extrapolation.

Enums

RbfKind

Radial basis function types.

SplineKind

Spline boundary conditions.

Functions

solve_linear_system

Solve A*x = b via Gaussian elimination with partial pivoting.