A Python package for numerical integration, providing a collection of easy-to-use functions for accurately approximating definite integrals.
The following is a list of the numerical integrations that can be found in the source folder:
adaptive_composite_simpson.py: Implements the adaptive composite Simpson's rule, which adjusts interval sizes to improve accuracy for functions with varying smoothness.adaptive_midpoint.py: Implements the adaptive midpoint rule, which dynamically adjusts the partition of the integration interval to enhance accuracy where the function changes more rapidly.adaptive_simpson.py: Implements the adaptive Simpson's rule, combining Simpson's rule with adaptive interval adjustments for better integration of non-uniform functions.adaptive_trapezoid.py: Implements the adaptive trapezoidal rule, which modifies interval sizes based on the function's behaviour to increase accuracy for complex integrands.composite_midpoint.py: Implements the composite midpoint rule, which divides the integration interval into subintervals and applies the midpoint rule to each for improved accuracy.composite_simpson.py: Implements the composite Simpson's rule, using multiple applications of Simpson's rule over subintervals to enhance the approximation of definite integrals.composite_trapezoid.py: Implements the composite trapezoidal rule, applying the trapezoidal rule over subdivided intervals to refine the precision of numerical integration.double_gauss_legendre.py: Implements the double Gauss-Legendre quadrature method, using orthogonal polynomials to compute integrals over complex functions and intervals accurately.gauss_legendre.py: Implements the Gauss-Legendre quadrature method, approximating definite integrals using points and weights derived from Legendre polynomials.midpoint.py: Implements the midpoint rule for numerical integration, approximating the area under a curve using each interval's midpoint.romberg.py: Implements Romberg's method, which refines the trapezoidal rule using Richardson extrapolation to achieve higher precision in numerical integration.simpson.py: Implements Simpson's rule, a numerical integration technique that approximates the integral using quadratic polynomials.trapezoidal.py: Implements the trapezoidal rule, estimating the integral by approximating the region under the curve as a series of trapezoids.