Sentence examples for by approximating the integral from inspiring English sources

Some operational matrices are obtained by approximating the integral of orthogonal polynomials.

In the SPH scheme, the properties associated with particle i are calculated by approximating the integral in Equation 8 by the sum A i = ∑ j Δ V j A j W r i − r j, h = ∑ j m j A j ρ j W r i − r j, h.

The fully discretized finite element equations are obtained by approximating the convolution integrals using a trapezoidal rule.

Also by using the trapezoidal rule for approximating the integral, the input voltage at time t = kT s is given by v k)=vleft k-1right)+a{e}_{omega}left(k-1right)+b{e}_{omega}left(k-2right) (29) a=vleft k-1right{T}_s}{2}kern0.75em,kern1.25em b=-{K}_p+a{ec{K_i{T}_{omega}left k-1right

Approximating the integral in (2.1) by the trapezoidal rule with step size h>0, we get f(t)approxfrac{he^{bt}}{pi}left(hat{f}(b)+2sumlimits_{k=1}^{infty}text{Re}left(hat{f}(b+ikh)right cos kht)right).

In this paper, we first obtain a similar approximation scheme to the Riemann Liouville fractional derivative with the convergence rate O k3−α), 0<α<1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials.

The method of approximating the integrals in (3.3) begins by integrating by parts to transfer all derivatives from y to S k.

Dubout and Fleuret solve this by approximating the root position of a part by rounding it to its closest integral position [29].

A Monte Carlo estimator approximates the integral or weighted sum of covariate and exposure histories.

An efficient algorithm approximates the integrals with sums over a finite number of orientations.

In addition, previous studies concentrated on the first digit, derived the deviation of the distribution under consideration from the NBL by calculating or approximating the respective integrals, and did not consider functions of random variables.