Environmental sustainability considerations are slowly being integrated into governing criteria and regulations in industrial and urban development worldwide.
Spontaneous crack propagation was simulated using a spectral form of the elastodynamic boundary integral equation, while steady-state solutions were obtained by numerically integrating the governing Cauchy singular integral equation.
The perturbation solutions are verified by numerically integrating the governing differential equations.
The perturbation results are verified by integrating the governing equation using a digital computer and an analogue computer.
The perturbation results are verified by integrating the governing equation with use of a digital computer and an analogue computer.
Finally, the remainder of the update step is taken, according to (X_{j}(t_{i+1}) = varphi_{Delta s^ (s,X_{j}(s))), where (Delta s^ = t_{i+1}-s), by integrating the governing equation for new region.
For the FE simulation, a weak form is obtained by integrating the governing equation in Eq. (6), and the heat flux can be calculated by averaging the specimen heat flux.
The Lax Friedrichs upwind splitting is used to update the PV moment in terms of a derivative Riemann problem, and a finite volume formulation derived by integrating the governing equations over each mesh element is used to predict the VIA moment.
In such modeling, the state (e.g. position and orientation in 3-dimensional space, biochemical activation or hydrolysis condition) of each primary component in a network of interactions is followed through time in a computer, typically using a large number of very small time-steps to integrate the governing system of differential equations.
We use a first-order scheme to numerically integrate our governing equation for dn/ dt given in Eq. (3), incorporating the effective velocity given in Eq. (2).
