Sentence examples for by numerical solution is from inspiring English sources

In the local WKB approximation for the cylindrical geometry the instability threshold (8) in the limiting case k y → ∞ is as follows (19)The comparison of the instability thresholds in the WKB approximation (19) and obtained by numerical solution is given in Fig. 6.

Predicted damaged zone by numerical solution are in good agreement with experimental observations.

Meanwhile, the rate of approximation to the true solution by the numerical solution is different for different numerical schemes.

Although the Poisson jump is concerned, the rate of approximation to the true solution by the numerical solution is the same as the equation in [15].

In Fig. 2, the exact solution is represented by solid line and the numerical solution is represented by dotted line at (K=1000) time level.

A generic problem formulation is presented in the format of a discrete-time optimal control problem whose numerical solution is achieved by use of a feasible-direction algorithm.

The numerical solution is approximated by a time stepping procedure and it has been implemented in the Symmetric Galerkin Boundary Element Method code.

Yet a different formulation leads to an open-loop constrained nonlinear optimal control problem, whose numerical solution is achieved by use of a feasible-direction algorithm.

Finally a numerical solution is achieved by a finite element analysis where generalized zero-thickness contact interface elements are adopted.

The numerical solution is implemented by using an operator split technique that utilizes an elastic predictor and dissipative corrector.

The accuracy of the numerical solution is enhanced by using non-uniform discretization steps and Richardson extrapolation.