A solar panel's power output over one hour is modelled by kW for in hours,

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Numerical and computational mathematics · Numerical and computational mathematics

Error, Chance and the Machine, Ch Integration: error expansions, Gauss rules and adaptivity

Problem

A solar panel's power output over one hour is modelled by

P(t)=\sin(\pi t/2)

kW for

t

in hours,

0\le t\le1

. The energy generated is

E=\int_0^1 P(t)\,\mathrm{d}t

kWh. ((a)) Compute the trapezium estimate

T

E

using two intervals (

h=0.5\,\mathrm{h}

). ((b)) Compute the leading Euler-Maclaurin correction term

\dfrac{h^2}{12}\left[P'(1)-P'(0)\right]

and use it to predict the sign and approximate size of the trapezium error

T-E

. ((c)) The exact value is

E=2/\pi\,\mathrm{kWh}

. Compute the true error and compare it with the prediction of part (b).

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