verry.integrate.cumulative_simpson

verry.integrate.cumulative_simpson(fun, a, b, n)

Cumulatively integrate fun using the composite Simpson’s 1/3 rule.

Parameters:

• fun (Callable) – Integrand. fun must be an univariate scalar-valued function.

• a (Interval) – Lower limit of integration.

• b (Interval) – Upper limit of integration.

• n (int) – Number of divisions.

Warning

fun must be a \(C^4\)-function on some open interval that contains a and b. Furthermore, fun must neither be a constant nor contain conditional branches (cf. Common pitfalls).

Examples

>>> from verry import FloatInterval as FI
>>> from verry import function as vrf
>>> s = cumulative_simpson(lambda x: x**2 + 2 * vrf.sqrt(x), FI(1), FI(2), 10)
>>> print(s)
[4.771236, 4.771237]