Sentence examples for by the exact solution from inspiring English sources

It is found that the deformation styles of the hydrogel samples are consistent with those described by the exact solution.

The approximation is verified by the exact solution of Nernst Planck Poisson set of equations.

The simple, but highly accurate solution was validated by the exact solution for the linear problem, and also by numerical method and differential transformation method in the case of the non-linear problem.

An independent solution has also been obtained by means of a finite element code in order to ascertain the validity and accuracy of the results predicted by the exact solution of Timoshenko's dynamic differential system.

After the numerical computation is verified by the exact solution in a special case and the numerical solutions in existing literature, numerical results of MSERR (mechanical strain energy release rate) and COD (crack opening displacement) are provided to discuss the fracture behavior.

The effects of the shear modulus, permeability and porosity of the soil medium and the velocity of the moving load on the dynamic response of the soil layer are numerically evaluated and compared with those obtained by the exact solution of the problem.

The existence of curve veering in continuous models is illustrated by presenting the exact solution of an elementary eigenvalue problem.

We investigate the nonlinear tunneling of optical solitons through both dispersion and nonlinear barriers by employing the exact solution of the generalized nonlinear Schrödinger equation with variable coefficients.

The natural frequencies and mode shapes of the plate are calculated by using the exact solution based on three coupled equilibrium equations.

Denote by (u_{e}) the exact solution and begin{aligned} U_{ N} xt)=mathcal{P}_{N} u_{e}(x,t).

By utilizing the exact solution to the 1D-TFIM, we can analytically calculate the FIM for a large number of spins.