Sentences with phrase «numerical solution»
A numerical solution refers to finding an approximate answer to a mathematical problem using calculations on a computer or calculator. It involves solving equations or finding values by performing mathematical operations rather than using a precise analytical method. Full definition
Their results are in excellent agreement with numerical solutions in 2 and 3 dimensions.
sciencedaily.com
A fourth grade teacher starts each class period by presenting a problem... along with its precise numerical solution.
They are different in exactly the same way as numerical solution is different from symbolic solution in mathematics.
Dan Hughes blog on numerical solutions of Lorenz equations is a good read.
An analytical model of subtropical mode water is presented, based on ventilated thermocline theory and on numerical solutions of a planetary geostrophic basin model.
When the geometry of such a system is specified, the simulator allows the user to vary primary and secondary scattering foil material and thickness and to see results in approximately 100 milliseconds, about 10 million times faster than Monte Carlo simulations, which are simulations and computational algorithms that rely on random sampling to obtain results for extremely complex problems that have only numerical solutions.
Using a semi-analytical method to find numerical solutions of the proposed model, they approximated various real - world scenarios.
The energy flux into each mode is predicted using a knife - edge topography that allows linear numerical solutions.
The numerical solution of the time dependent Schrödinger equation for the investigated atoms in a strong laser field provided excellent agreement of the theory with the experimental data in both regimes.
What is surprising in this method is that the mathematics of shape, in the form of what differential - geometers call the curvature flow, is coupled with techniques that originated in the numerical solution of partial differential equations to deblur and denoise an image.
The principle of the first method lies on the numerical solution of Newton's equations of motion to propagate the system, whereas the second stochastically generates states of a system according to a predetermined statistical mechanical probability distribution.
It is critical that the actual coding be shown to be exactly what was intended as guided by theoretical analyses of the discrete approximations and numerical solution methods.
Figure 2: The numerical solutions of Lorenz» equations plotted in the same coordinate system.
These are extremely detailed and consequently the numerical solution to the equations require days or weeks of computational time.
But if your answer is a discourse on the failure of GCMs, then «it's obvious to me» (there's that phrase again) that you haven't understood the difference between a GCM and the numerical solution to a radiative balance equation.
An even better example of a chaotic system still open to numerical solution is the motion of the astroids in the solar system.
The people who utter the D word do not care about what the objects of their ires actually think: because the issue is not one's opinion on the GHG properties of CO2, and not even what the temperature record says, or what the equations may indicate, or how good the numerical solutions we call Models are.
From what I read here there is a great deal of understanding, in depth, of the complexity of both the physical phenomena and processes, the mathematical problems associated with both the continuous and discrete equations, numerical solution methods for the latter, and designing, developing, building, testing, and applying computer software that has all this stuff in it.