Sentence examples for estimates of order from inspiring English sources

Error estimates of order O h3/2) are established in the discrete inf sup stability norm which includes the mesh-dependent weighted advective derivative.

In Section 3, we introduce two kinds of auxiliary obstacle problems and two enriching operators and obtain error estimates of order (O(h)) in the energy norm.

This paper shows that a certain kernel estimate of a semigroup implies the Lp-spectral independence of the generator, generalizing the case of upper Gaussian estimate and "Gaussian estimate of order α∈ 0,1] [S. Miyajima, H. Shindoh, Gaussian estimates of order α and Lp-spectral independence of generators of C0-semigroups, Positivity 11 (1) (2007 15 39]], Definition 3.1".

It is obtained by successive simplifications justified either experimentally (from observations, estimates of orders of magnitude) or by an analysis of governing equations (through asymptotic developments and changes of variables).

Fitted line reflects a locally linear nonparameteric estimate of order, error bars reflect conditional MSE estimates.

It should be also noted that when (alpha =2) (7) becomes a uniform Markov type estimate of order (n).

Finally, we derive an optimal error estimate of order (O(h)) in the broken energy norm successfully by a different approach from the existing literature.

In 2009, Yuan et al. [9], improved their results and gave a general estimate of order of w z), which depends on the degrees of coefficients of differential polynomial for w z).

Since the exact solution u ( t ) is sufficiently regular over Ω, it follows from Remark 3 that the theoretical error estimates are of order O ( h p + τ ).

Theoretical estimate of ordering and modulus contribution to strengthening suggested that ordering had a dominant influence on strength.

In order to show the time decay of the solutions obtained above, we need the refined energy estimates of each order derivatives of the solutions to the system (1.4).