Sentence examples for using the nonlinear solution from inspiring English sources

Stress intensity factors induced by the electrostrictive strains are evaluated using the nonlinear solution of the electric displacements.

Iwaniec and Sbordone realized that the usual Sobolev assumption for weak solutions to p-harmonic equation can be relaxed to a slightly weaker Sobolev space and proved that very weak solutions are actually classical weak solutions by using the nonlinear Hodge decomposition to construct suitable test functions.

The existence of nontrivial solution was established by using the nonlinear alternative of Leray-Schauder.

The solution to this equation was fitted to the experimental data points using the nonlinear estimation routine in Statistica (StatSoft Inc, Tulsa OK) or the solver in Microsoft Excel.

It is found that: for large heat deposition rates the use of the nonlinear solution is uniquely necessary to assess the thermal and optical characteristics, high pumping loads require cryogenic cooling to maintain low thermal lensing and thermally induced dioptric power depends quadratically on the heat rate.

The nonlinear solutions are computed using the Newton Raphson iteration method.

This figure gives a clear example that it is dangerous to make any conclusions about the long-term behavior of the nonlinear system using the exact solutions of the approximate linear system.

This work develops exact finite-difference schemes for the two-dimensional nonlinear coupled viscous Burgers equation using the analytic solution.

Incremental and total formulations are used to arrive at the proper nonlinear solution of the governing equations.

Recently, many results were obtained dealing with the existence of solutions for nonlinear fractional differential equations by using the techniques of nonlinear analysis; see [1 23] and references therein.

with some quite general nonlinear boundary conditions by using the lower and upper solution method.