Numerical integration algorithms sample the integrand at a finite number of points. Consequently, they cannot guarantee accurate results (or accuracy estimates) for arbitrary integrands and …

Integration and ODEs (scipy.integrate) # Integrating functions, given function object # ... Integrating functions, given fixed samples # ... See also scipy.special for orthogonal …

For weighted integrals with finite integration limits, the integration is performed using a Clenshaw-Curtis method, which uses Chebyshev moments. For repeated calculations, these moments …

For each level of integration, qagse is used for finite limits or qagie is used if either limit (or both!) are infinite. The following provides a short description from [1] for each routine.

Cartwright, Kenneth V. Simpson’s Rule Cumulative Integration with MS Excel and Irregularly-spaced Data. Journal of Mathematical Sciences and Mathematics Education. 12 (2): 1-9

If x is provided, the integration happens in sequence along its elements - they are not sorted. Integrate y (x) along each 1d slice on the given axis, compute ∫ y (x) d x.

Default is None, which means res has one element less than y along the axis of integration. Returns: resndarray The result of cumulative integration of y along axis. If initial is None, the …

For each level of integration, qagse is used for finite limits or qagie is used, if either limit (or both!) are infinite. The following provides a short description from [1] for each routine.

Wraps quad to enable integration over multiple variables. Various options allow improved integration of discontinuous functions, as well as the use of weighted integration, and generally …

ode # class ode(f, jac=None) [source] # A generic interface class to numeric integrators. Solve an equation system y ′ (t) = f (t, y) with (optional) jac = df/dy. Note: The first two arguments of f(t, …