Sentence examples for associated solution of the from inspiring English sources

Suppose, by contradiction, that equation (3) is nonoscillatory and let w be a solution of the associated Riccati equation (6) and v = h p w - G the associated solution of the modified Riccati equation (9).

where K ( 1 ) is an integration constant associated with the solution of the previous equation.

where K ( 2 ) is an integration constant associated with the solution of the previous differential equation.

In order to reduce computational costs associated with the solution of the ensuing system of simultaneous equations, the HFGMC global system of equations for doubly-periodic RUCs was reduced in size through the use of Proper Orthogonal Decomposition.

The major advantage of the present method is to remove numerical difficulties associated with the solution of the Hamilton Jacobi equations in most conventional level set methods, such as the CFL condition, the regularization procedure to retain a signed distance level set function and the non-differentiability related to the Heaviside and the Delta functions.

The degrees of freedom and the numbers of nonzero entries of the solution matrices (NNZ) for the various meshes in the simulations give some insight into the computational workload associated with the solution of the monodomain problem using spectral elements for a given degree of accuracy.

This article presents a new hybrid formulation and associated numerical procedures for solution of the BTE for phonons.

Based on the local quadratic approximations of a dispersion surface, where the radian frequency is considered as a function of wave vector components, we deduce properties of a transient asymptotic solution associated with the contribution of the point source to the wave form.

When the initial data is a sum of such quadratic oscillations, we prove that the associate solution is the superposition of the nonlinear evolution of each of them, up to a small remainder term.

We are concerned with the existence of uniform attractors for the process associated with the solutions of the following non-autonomous p-Laplacian equation: u t − Δ p u + | u | p − 2 u + f ( u ) = g ( x, t ), ( x, t ) ∈ Ω × R. (1).

Therefore, they were solely related to a certain "optimal" solution associated with the application of the minimum-norm/least-squares inverses to an Eigen matrix obtained from the factorization process [11].