Sentence examples for by solving the partial from inspiring English sources
The temperature fields are determined by solving the partial differential equation of heat conduction in a VGF crystal growth system.
By solving the partial differential equations (PDEs) that describe how the coordinates transform, three-dimensional (3-D) electromagnetic and acoustic invisible cloaks with arbitrary shapes can be designed provided the boundary conditions of the cloaks can be determined by the corresponding transformation.
A dispersion model has been formulated that includes the effects of gas and particle mixing, fluid-to-particle heat transfer and intraparticle thermal conductivity, and the dynamic thermal response in theory has been found by solving the partial differential equations in the Laplace transform domain.
We have derived (9) by solving the partial differential equation.
The exact shape of the decay law can be obtained by solving the partial differential equations that describe molecular diffusion and population decay.
The traveling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver.
The results obtained by path integral methods turn out to be the same as those obtained previously by solving the parabolic partial differential equation for the fourth moment.
The shape functions with up to third order nonlinear terms of generic nodal displacements are obtained by solving the nonlinear partial differential equations of motion in a quasi-static sense.
In the latter case, the front has a unique velocity that is obtained by solving the associated partial differential equation (PDE) in traveling wave coordinates.
Macroscopic flow properties were investigated by solving the coupled partial differential equation model under different modes of operation.
By applying the classical implicit format solving the partial differential equations and the method of steps for differential difference equations,we provide a numerical example to show the theoretical results.
