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Using the discrete energy method, we prove the compact difference scheme is unconditionally stable and convergent.
The stability and convergence of the scheme are proven using the discrete energy method.
In this paper a technique for a quantum computer architecture is demonstrated using the discrete energy levels of an impurity doped semiconductor to represent the quantum computational basis.
By using the discrete energy method, we prove that the ADI scheme is unconditionally stable and the numerical solution converges to the exact one with order O k+h2x+h2y), where k is the temporal grid size and hx,hy are spatial grid sizes in the x and y directions, respectively.
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Solution of the time-dependent radiation transport equation is obtained using the discrete ordinates method and the energy flow into the Lagrangian meshes as a result of radiation interaction is fully accounted for.
Thermal activation is described as a hopping process over a multidimensional energy landscape using the discrete orientation model limit of the Landau Lifshitz Gilbert dynamics.
Using the discrete optimization algorithm, the curves of energy efficiency for the optimal CT and DT systems, which are expressed by "Optimal C" and "Optimal D", respectively, are plotted in Figure 5.
The discrete-time control rules which correspond to potential energy shaping and damping assignment are designed directly using the discrete time model of the desired system and the discrete time model of the open loop systems.
The distribution of impact energy is obtained from the simulation of the charge motion using the discrete element method.
The radiative heat flux in the energy equation is obtained using the discrete-ordinates solution of the radiative transfer equation.
It is easy to see from Figure 2 that scheme (2.6) preserves the discrete mass and the discrete energy very well, thus it can be used for computing for a long time.
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