Sentence examples for by numerical integration is from inspiring English sources

Miller (1964) recognised that obtaining the solution to an N-body problem by numerical integration is difficult.

The external current density, obtained by numerical integration, is J t = ∫ 0 D j eμ, hμ x, t + j d x, t dx.

For any sufficiently complex model, the speed and accuracy of solving the ODEs by numerical integration is critical.

The system response obtained by numerical integration was treated as modal analysis data and the result is that the kurtosis-optimized excitation has compensated for the effect of nonlinearity and allowed to identify the damping ratio with good precision whereas an ordinary Gaussian excitation with randomized phases caused an error of 75percentt.

In a multiphase flow such as gas and dust, the time step for numerical integration is controlled by the Courant condition, by the drag between the fluids, and by gravity.

By assuming realistic initial values, numerical integration is carried out for a sufficient number of heart cycles to achieve steady-periodic values for every parameter.

The numerical integration is performed by a compiled Fortran 95 program that is run by the Excel VBA program.

To account for the fine scales of the problem, elementwise numerical integration is replaced by micro FE methods on sampling domains.

Adjusting the active DEs dynamically during the time integration is the most significant feature of the G-Scheme, since the numerical integration is accomplished by solving a number of DEs typically much smaller than the dimension of the original problem, with corresponding saving in computational work.

Note that the numerical integration is typically computed by convolution in the previous work [13, 14].

Since the equations are lengthy, they are described in Additional file 1. Numerical integration was performed by using GRIND [ 43].