Examples of 'analytical solutions' in a sentence
Meaning of "analytical solutions"
Analytical solutions are solutions or answers to problems or equations that are obtained through using analytical methods, such as mathematical calculations or logical reasoning
How to use "analytical solutions" in a sentence
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analytical solutions
Provision of analytical solutions or audience measurement statistics.
Simulations are also used to verify analytical solutions.
A number of analytical solutions to this problem are available.
The numerical results are compared with analytical solutions.
Analytical solutions in the grain industry.
Rapid creation of analytical solutions.
Delivers analytical solutions for the retail industry.
Develop predictive analytical solutions.
The analytical solutions are possible in simplified situations only.
And selection of analytical solutions.
Special analytical solutions for all are also constructed.
Early results are very promising when compared to analytical solutions.
Analytical solutions of drag and lift have been proposed.
Absence of analytical solutions.
Analytical solutions exist for such models in simple flows.
See also
They were followed by analytical solutions for the dairy industry.
Analytical solutions are given.
Configuration of analytical solutions.
New analytical solutions in oncology.
The results show good agreement with analytical solutions or correlations.
All the analytical solutions are compared with the numerical simulations.
To reduce the risks associated with initiatives to implement analytical solutions.
No exact analytical solutions are possible.
The solutions developed were validated by comparison with results provided by analytical solutions.
Improved analytical solutions.
Analytical solutions for certain systems of equations can be difficult or impossible to obtain.
Intelligent analytical solutions.
Such analytical solutions are limited to relatively simple flow systems and reactions.
It is very difficult to find analytical solutions for this transient behavior.
Analytical solutions and algorithms are proposed for these two types of models.
This allows for otherwise unavailable analytical solutions to the distortion.
Theoretical and analytical solutions have been proposed to solve the studied problems.
I then carefully test my module by comparing my results with known analytical solutions.
Obtain analytical solutions of which the effectiveness can be verified by numerical solutions.
The basic model predictions agree perfectly with the analytical solutions.
Some simple models are based on analytical solutions that require many simplifying assumptions.
A discussion follows on some particular features and limitations of the analytical solutions.
Analytical solutions in terms of statistiscal mechanics are extremely hard to obtain for theses systems.
There are some advances made in finding analytical solutions for the charge.
Analytical solutions can not be considered for such problems owing to their complexity.
We have also calculated the muon density using our analytical solutions.
Analytical solutions are obtained using lévy formalism of characteristic functions and compared with empirical data.
These both aspects contribute to renew widely the interest for analytical solutions.
All analytical solutions of diquat and paraquat have been prepared and stored in polypropylene vessels.
Results have been verified and validated through the comparison with analytical solutions.
Add a third mass point there are no analytical solutions except in some very special circumstances.
The perfect link between researchers and manufacturers of the best analytical solutions.
Analytical solutions are obtained for the case that the total amount of heat is conserved.
Excellent agreement has been obtained between the numerical predictions and analytical solutions.
Corrections to the analytical solutions have already been proposed to account for the vadose zone.
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There are no simple solutions to this oversight lacuna
Solutions do not seem too difficult to find
There were no ready solutions to either of those problems
