Sentence examples for by direct numerical integration from inspiring English sources

All analytical solutions have been verified by direct numerical integration of the modal equations of motion.

The results are in excellent agreement with those obtained by direct numerical integration of the governing partial differential equations.

A particular solution instability is found to exist using Hsu's method and is verified by direct numerical integration.

All analytical predictions are compared with those which are obtained by direct numerical integration of system equations.

The perturbation results are validated by direct numerical integration of the equations of motion and Floquet theory.

The coupled electro-mechanical equation of motion is derived using the extended Hamilton's principle, and it is solved by direct numerical integration method.

The validity of the stability diagram is verified by direct numerical integrations of the equations of motion of the system.

Although the problem could be approached by a direct numerical integration, e.g. by Monte-Carlo simulations, because of the stochastic nature of the excitation, this would imply a large number of runs to produce results of some statistical significance.

This equation is solved by employing direct numerical integration method.

By a direct numerical integration of the dynamical evolution equations, we study phase separation of thin polymer blend films in two-dimensional models.

The coupled partial differential equations of motion are derived by use of Hamilton's principle and Galerkin's method is used to reduce the governing equations to a system of nonlinear ordinary differential equations in time, which are then solved by a direct numerical integration method.