An iteration for the terminal velocity of a falling sphere with quadratic drag…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Numerical and computational mathematics · Numerical and computational mathematics

Error, Chance and the Machine, Ch Iteration: nonlinear systems and eigenvalues

Problem

An iteration for the terminal velocity of a falling sphere with quadratic drag produces the following sequence of absolute errors ek=∣vk−v∗∣e_k = |v_k - v^*| (in m s−1\mathrm{m\,s^{-1}}): e0=1.0×10−1e_0=1.0\times10^{-1}, e1=5.0×10−3e_1=5.0\times10^{-3}, e2=1.25×10−5e_2=1.25\times10^{-5}, e3=7.8125×10−11e_3=7.8125\times10^{-11}. Assuming the errors obey ek+1=C ek pe_{k+1} = C\,e_k^{\,p} for constants CC and pp, estimate the order pp using the last three entries of the sequence, and state which standard method this order identifies.

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