Sentence examples for order expansions from inspiring English sources

Linear and higher order expansions (fourth-order) are introduced for displacements and stresses in the thickness plate directions.

Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space.

A fourth and fifth order expansions are used respectively for the transverse and tangential displacement of the core to model the core compressibility effect.

Linear case (N = 1) permits us to obtain classical beam theories while higher order expansions can lead to three-dimensional description of dynamic response of blades.

However, the scalar method is shown to be more CPU efficient for high order expansions, in addition to requiring less storage.

In this case, we can avoid the complicated technique necessitated by the Strang-type high order expansions.

It is observed that the first order expansion suffices to yield accurate results.

In both cases, the second order expansion is sufficient to model the uncertainties in growth rate.

For sufficiently "weak" coupling, a low order expansion in powers ofĜ0Vprovides the solution according to Rayleigh Schrödinger perturbation theory.

The method of multiple scales is used to determine a fourth order expansion of the galloping amplitude of cantilever beams.

The algorithm reduces the CPU time dependency on expansion order p from O p2) of the classical treecode to be lower than a linear dependency in pmax, where pmax is the maximum expansion order used in the variable order expansion.