This auxiliary equation is used for instance by Stratton in his 1935 article.
2.
Since the Parker Sochacki method involves an expansion of the original system of ordinary differential equations through auxiliary equations, it is not simply referred to as the power series method.
3.
Expanding the ODE problem with auxiliary variables produces the same coefficients ( since the power series for a function is unique ) at the cost of also calculating the coefficients of auxiliary equations.
4.
Realizing that this can be used to find the heat transferred ( Q ), which was used in the definition, and using the view factors as auxiliary equation, it can be shown that the Gebhart factors are:
5.
A more efficient version of the algorithm is the extended Euclidean algorithm, which, by using auxiliary equations, reduces two passes through the algorithm ( back substitution can be thought of as passing through the algorithm in reverse ) to just one.
6.
More generally, if an equation of prime degree with rational coefficients is solvable in radicals, then one can define an auxiliary equation of degree, also with rational coefficients, such that each root of is the sum of-th roots of the roots of.
7.
In the theory of differential equations, "'comparison theorems "'assert particular properties of solutions of a differential equation ( or of a system thereof ) provided that an auxiliary equation / inequality ( or a system thereof ) possesses a certain property.
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