Sentence examples for using the exact solutions from inspiring English sources

This includes the difficulty of using the exact solutions and the unwanted fluctuations, which arise in the numerical results.

The right-hand side functions and boundary conditions can be obtained by using the exact solutions.

The right-hand side functions and the Dirichlet boundary conditions are determined using the exact solutions.

By using the exact solutions and bifurcations of this sub-equation which was derived in [23], some new traveling wave solutions and quasi-periodic traveling wave solutions of the KdV-Sawada-Kotera-Ramani equation are derived in Section 2.

This figure gives a clear example that it is dangerous to make any conclusions about the long-term behavior of the nonlinear system using the exact solutions of the approximate linear system.

Proposed formulation is verified using the exact solution of Kovasznay flow.

The natural frequencies and mode shapes of the plate are calculated by using the exact solution based on three coupled equilibrium equations.

In the next step, the curvature effect is included and the SMA helical spring is analyzed using the exact solution presented for torsion of curved SMA bars.

Stiffness matrix, consistent load vector, and mass matrix of a beam element is obtained using the exact solution of the governing equations.

For high density insulation materials, such as brick and concrete, the resulting temperature in a structural steel member using the EC3 procedure differs from that using the exact solution for heat transfer analysis.

The time-averaged acoustic power transmitted in the duct is formulated by using the exact solution for the wave modes in the duct in the proposed definition of acoustic intensity.