Sentence examples for modified equations are from inspiring English sources

The modified equations are first verified with a known material and then used for sandwich composites.

The general equations (4) for chain decays show a time dependence given by sums and differences of exponential terms, though special modified equations are required in the unlikely case that two or more decay constants are identically equal.

Some properties of the associated modified equations are proven and then extended to the semi-discrete case.

New modified equations are developed to describe the relation between partial pressure and mole fraction, and an approximate analytical solution for heat transfer coefficient in the presence of non-condensable gas is obtained.

This deficiency is rectified in three steps: the equations of the semi-implicit linear method are modified, the modified equations are incorporated into Newton's method to solve nonlinear equations, and the transfer equations are solved by the resulting method.

Flügge's modified equations are used to describe shell motions, taking into account the steady viscous forces due to flow pressurization and traction effects on the shell; these equations are subsequently solved by the finite difference method.

The method of modified equations is used to explain failings of Euler-based methods.

Vector field plot of modified equations is qualitatively similar to Figure 2C.

Since the modified equation is difficult to solve analytically, we make use of the numerical scheme to solve this new equation.

Our implementation is based on modified equations that are derived by applying the filter after every time step in a simple first-order time integration scheme.

In particular, the form of the analytical solution for linear modified equations can be solved exactly.