This technique is based on the discrete-event simulation (DES) methodology for nonlinear flux-conservative PDEs [Y.A. Omelchenko, H. Karimabadi, Self-adaptive time integration of flux-conservative equations with sources, J. Comput. Phys. 216 (1) (2006) 179–194].
In general, methods requiring the integration of fluxes and/or ODEs (i.e. IFPE, IFPE-ODE, IPE-ODE and SPE-ODE) took longer to converge than the rest.
Considering that a solitary wave will go through the fission process over a long obstacle or step, during which the wave profile continuously evolves that makes it difficult to define the transmission coefficient based on wave heights, we propose the integration of energy flux for the calculation of wave coefficients.
The total power absorbed by the single Au NP, P abs,Au, was calculated by integration of photon flux over a closed surface surrounding the NP PP abs, Au ω = ∫ 1 2 ω E ω, x, y, z 2 ε Au ω dV (1). in which ω, ε Au, and |E| are the frequency of the light, the imaginary part of the Au permittivity, and the magnitude of the electric field, respectively.
The advantages of the IFPE over the IPE come at the cost of increased computational time due to the numerical integration of reaction flux equations.
Meanwhile, the cost per iteration is associated with the integration of reaction flux functions, the inner optimization, and in the case of IFPE-ODE, the integration of ODE model.
An integration of interdiffusion fluxes at a selected section over time or of the interdiffusion fluxes over a region in the diffusion zone can be determined by using the transfer matrix method.
An operational use of the actual evapotranspiration assessed by remote sensing approaches requires the integration of instantaneous fluxes to daily values.
Integration of the solids flux profile gave the external solids circulation rate, in reasonable agreement with measurements external to the riser.
A precise determination of the flow resistance between the spatial node points in the numerical solution scheme is obtained for even extremely compressible solids by integration of the liquid flux equation with respect to cake thickness.
