The phrase "although this approximation" is correct and usable in written English.
It can be used to introduce a contrast or exception regarding an approximation being discussed in a text.
Example: "Although this approximation simplifies the calculations, it may not accurately reflect the true values."
Alternatives: "even though this estimate" or "despite this approximation".
Although this approximation does not produce exactly the same values of all the variables at some time in the future as those produced by a numerical solution of the differential equations starting with the same initial conditions, the qualitative behaviour is indistinguishable over long time periods.
Although this approximation would also be inaccurate, it is an improvement over the first one because the intervals during which the velocities of the particles are erroneously presumed to be constant are shorter in the second calculation than in the first.
Although this approximation simplifies the mathematical problem, it is only possible under certain circumstances.
Although this approximation rate is not considered final, to our knowledge it is the first general, nontrivial result of this type.
Although this approximation is valid in the case of pure radiative transfer problems, the Sauter diameter is reconfirmed to be the appropriate diameter for approximating problems in radiative heat transfer, although volume length mean diameter shows better accordance in some cases.
Although this approximation is known since de 90's, it is noteworthy and remarkable that so few laser beams have ever been described with it [ 28– 30].
Although we see that this approximation converges, the peaks often do not occur at the correct locations, as opposed to the approximations resulting from the zero-pole interpolation (compare to Figure 8).
Although the impact of this approximation cannot be analyzed theoretically, the numerical results in Figure 4 show that the mismatch between the proposed analytical approximation of the RMSE and the RMSE obtained by direct simulation of the communication system is larger in the low SNR region.
This approximation, although not capturing the molecular interactions in atomistic detail, can represent many salient aspects that have been ignored in previous work on speciation theory.
Although the quality of this approximation can only be assured by the Central Limit Theorem asymptotically, (i.e. for arbitrarily large sample sizes), we have followed standard practices to promote acceptably accurate approximations[ 39].
Although we demonstrate that this approximation converges to the exact solution in the one-population case, we do not have an equivalent demonstration for the case of the migration events at boundary.
