All of them allow one to compute a numerical approximation of the solutions by solving one or several univariate equations.
22.
If you allow numerical approximations, then how precise does it need to be to count as a " solution "?
23.
However, root-finding algorithms may be used to find numerical approximations of the roots of a polynomial expression of any degree.
24.
Suppose that instead one has equations of motion, or possibly only numerical approximations of these, but " not " the Hamiltonian.
25.
A considerable number of popular empirical models turn out to be special cases of the DEB model, or very close numerical approximations.
26.
The equation hasn't been solved except by numerical approximations for anything more complicated than a hydrogen atom-- one proton and one electron.
27.
A way to calculate nitrogen transformation rates in soil can be achieved by numerical approximation that takes different, simultaneous nitrogen transformations into account.
28.
To overcome this, one uses some sort of numerical approximation of the derivatives, see for instance the finite element method or finite differences.
29.
Which is asymptotically correct as n tends to infinity ( and hopefully also gives good numerical approximations for reasonable-sized values of n ).
30.
"' Numerical methods for ordinary differential equations "'are methods used to find numerical approximations to the solutions of ordinary differential equations ( ODEs ).
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