The phrase "auxiliary solution" is correct and usable in written English.
It can be used in contexts where a secondary or supportive solution is being discussed, often in technical or problem-solving scenarios.
Example: "In addition to the primary method, we should consider an auxiliary solution to address potential issues."
Alternatives: "supporting solution" or "secondary solution".
Their results, however, strongly rely on the knowledge of the auxiliary solution (z(t)).
In order to reduce the cost of flux correction, the raw antidiffusive fluxes are linearized about an auxiliary solution computed by a high- or low-order scheme.
Besides, it is not necessary to find vibration modes or an auxiliary solution (such as quasi-static solution) that are required in most of the approaches given in previous technical publications considering the case of base excitations.
By virtue of the Kolosov Muskhelishvili potentials of 2D isotropic elasticity, the auxiliary solution of the half-plane problem is derived in terms of the boundary integrals in the inclusion domain.
Step 1 (existence of auxiliary solutions ).
Generalized analytical formulas are established which relate the exact solutions to corresponding time-independent auxiliary solutions.
Our solution technique fully exploits as auxiliary solutions the ones for the corresponding plane-strain and anti-plane shear problems by reducing the original 3D problem to two separate 2D problems.
Since no extra auxiliary solutions are required for the computation, the proposed method appears to be versatile and can be used for evaluation of the stress intensity factors associated with crack front and crack surfaces of arbitrary curvatures.
In particular, it is then more transparent to construct solutions by means of Euler method and the auxiliary solutions (vartheta ^f_{{mathbf g}, u, w} : [0,1] times L^p({{mathbb R}^{N}}) rightarrow L^p({{mathbb R}^{N}})) to autonomous linear problems specified in Proposition 29.
Then various models consisting of ideal assumptions, governing equations, auxiliary conditions, solution methods and main results are presented.
A gel coating on the silver electrode could replace both the salt bridge and the auxiliary electrochemical solution.
