Sentence examples for by numerical approximation is from inspiring English sources

For the resulting approximate pivot, we show that under mild conditions the error induced by numerical approximation is op(1/n).

A time dependent inverse source problem with additional measurement data at an inner point for the fractional diffusion equation is investigated and stable and accurate numerical approximation is obtained by means of the boundary element method and the first order Tikhonov regularization.

The details of the numerical approximation are as follows.

Equation (2) cannot be transformed to directly obtain the d ± x% values, rather a numerical approximation was required.

In the general case, numerical approximations are necessary.

Numerical approximations are then used to explore the effects of the end restraint provided by the end frits.

Hence, numerical approximations are needed.

end{aligned} In general, Eq. (16) has to be solved by numerical approximation, however, it only needs to be precomputed once for the step-size Δt.

The integration problem is now simplified to the problem of integrating w.r.t. a scalar parameter β, which is relatively easily handled by numerical approximation using the composite trapezoidal rule.

The presented solution could eventually be used to validate those found by numerical approximation techniques.

Eventually, it could be used to validate those found by numerical approximation techniques.