Sentence examples for by the linear solution from inspiring English sources

In the previous section, we have shown that the solution u to the problem (1.1), (1.2) can be approximated by the linear solution u L. In what follows, we shall derive a simpler asymptotic profile of the linear solution u L. Let v be the solution to the initial data problem v t − β v x x = 0, t = 0 : v = ( u 0 + u 1 ) ( x ).

The deficiency of the linear solution is illustrated by its inability to capture essential features of the equilibrium problem particularly near and above the critical speed.

This MSE is again lower than the one obtained by the strictly linear solution, given by[20] MSE DFE = exp 1 N ∑ n = 1 N log 1 1 + γ | H n | 2. (44).

Results show that the singular stress field predicted by the linear elastic solution for the rigid inclusion model can be generated in reality, with great accuracy, within a material.

Resulting responses of the symmetric and asymmetric cable trusses with various geometries (shallow and deep profiles) obtained by the present non-linear closed-form solution are compared with those obtained by Irvine's linear solution and those by the non-linear finite element method.

The J-integral values obtained by the linear-elastic solution (22) at various E f0/E c0 ratios for E c1/E c0 = 2, E f1/E f0 = 0.8 and 2h 2/h = 3/4 were presented also in Fig. 5 in non-dimensional form in order to evaluate the influence of material non-linearity on the mode II fracture behaviour.

A well known mesh condition for the DMP satisfaction by the linear finite element solution of isotropic diffusion problems is the non-obtuse angle condition that requires the dihedral angles of mesh elements to be non-obtuse.

The desired solution is obtained by the linear combination of the solutions of the differential and algebraic parts.

The numerical method is based on the approximation of all the solutions by the linear combination of some well chosen solutions computed for some particular values of R, the same ones for every variable: u, θ, P.

By properly superposing the linear elastic solutions of flat and cylindrical indentations, the approximate solution to the adhesive JKR contact state between elastic films coated on rigid cylinders was also obtained, of which the relations between applied force, penetration depth, and contact width were expressed in terms of the geometric parameters and elastic constants of the two elastic films.

We address this problem by extending the linear programming-based solution introduced by Goldman et al.[14] to EC prediction.