maths.numerical_analysis.simpson_rule¶
Numerical integration or quadrature for a smooth function f with known values at x_i
This method is the classical approach of summing ‘Equally Spaced Abscissas’
method 2: “Simpson Rule”
Functions¶
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Calculate the definite integral of a function using Simpson's Rule. |
Module Contents¶
- maths.numerical_analysis.simpson_rule.f(x)¶
- maths.numerical_analysis.simpson_rule.main()¶
- maths.numerical_analysis.simpson_rule.make_points(a, b, h)¶
- maths.numerical_analysis.simpson_rule.method_2(boundary: list[int], steps: int) float¶
Calculate the definite integral of a function using Simpson’s Rule. :param boundary: A list containing the lower and upper bounds of integration. :param steps: The number of steps or resolution for the integration. :return: The approximate integral value.
>>> round(method_2([0, 2, 4], 10), 10) 2.6666666667 >>> round(method_2([2, 0], 10), 10) -0.2666666667 >>> round(method_2([-2, -1], 10), 10) 2.172 >>> round(method_2([0, 1], 10), 10) 0.3333333333 >>> round(method_2([0, 2], 10), 10) 2.6666666667 >>> round(method_2([0, 2], 100), 10) 2.5621226667 >>> round(method_2([0, 1], 1000), 10) 0.3320026653 >>> round(method_2([0, 2], 0), 10) Traceback (most recent call last): ... ZeroDivisionError: Number of steps must be greater than zero >>> round(method_2([0, 2], -10), 10) Traceback (most recent call last): ... ZeroDivisionError: Number of steps must be greater than zero