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There has been extensive development of algorithms to solve differential equations numerically, and in most contexts the difference between an analytical solution and the approximate numerical solution is inconsequential.
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Although not shown here, the agreement between the simulation and the analytical solution in other cases (the other station array and/or different weights) becomes better than that of Fig. 2. We have only discussed qualitative relations between the parameters, so an analytical solution is an appropriate approach to this issue.
This work reports such an analytical solution for brittle interfacial cracking between two dissimilar elastic layers.
We do not have an analytical solution to the question on correlation between the speed of movement in the parameter space and the width of the distribution.
Due to the nonlinear relationship between measurement variables and state variables, it is difficult to have an analytical solution.
This gives our equation an analytical solution.
It was evaluated by an analytical solution.
TA: Why do you need an analytical solution?
An analytical solution to the relationship between recovery and imbibition time for linear spontaneous imbibition has also been derived in the case in which gravity is ignored.
A good agreement was observed between the analytical solution and the experimental data indicating that the approach provides a reasonable and conservative estimation of the impact resistance of the sandwich beams.
Comparisons between the analytical solution and test results validated the proposed formula.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com