Sentence examples for numerically approximating from inspiring English sources

While these theories enable us to define weak solutions to nonconservative hyperbolic systems, difficulties arise when numerically approximating these systems.

The present article aims at highlighting the strengths and weaknesses of the so-called spectral-like optimized (explicit central) finite-difference schemes, when the latter are used for numerically approximating spatial derivatives in aeroacoustics evolution problems.

Approaches for numerically approximating the solution of fractional differential equations have been extensively studied; see, e.g., [38 42].

The coefficients and are determined numerically, approximating all the reference wideband codecs in a least-squares sense.

A closed form solution for the maximized weights is not known to these authors, so the weights are found by numerically approximating the weights that maximize Equation 14.

Numerically approximating solutions to nonlinear conservation laws requires applications of a conservative and stable numerical method, so that reasonable numerical solutions are obtained, such that positivity and/or monotonicity of certain physical quantities are realized.

As the pioneer in numerical methods for such equations, Akrivis et al. [5] numerically approximated the solution of a prototype ultraparabolic equation by applying a fixed-step backward Euler scheme and a second-order box-type finite difference method.

The space derivatives are numerically approximated by means of differentiation matrices.

One of the examples is analytical, while in the remaining two examples the controller is numerically approximated.

A nonlinear shooting method using Newton's iterations with numerically approximated tangent is designed for the solution of the problem.

Surprise can often be computed analytically, for instance in the case of distributions from the exponential family, or it can be numerically approximated.