Integration
To achieve a definite integration of functions on suitable domains, we have mainly two methods—Numerical integration and Symbolic integration.
Numerical integration refers to the approximation of a definite integral by a quadrature process. Depending on how the function f(x) is given, the domain of integration, the knowledge of its singularities, and the choice of quadrature, we have different ways to attack this problem:
- For univariate polynomials, exact integration is achieved algebraically on each finite interval
- For functions given as a finite set of samples over their domain:
- The composite trapezoidal rule
- Simpson's trapezoidal rules
- Romberg integration scheme
- For generic univariate functions given as Python functions, on finite intervals:
- Fixed-order Gaussian quadrature
- Fixed-tolerance Gaussian quadrature
- Simple non-adaptive quadrature, by applying 21-, 43- and 87-point Gauss-Kronron rules
- Simple adaptive quadrature, by subdivision and quadrature on each subinterval...
