“…The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. …”
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“…Why geometric numerical integration? In their article of the same title Arieh Iserles and Reinout Quispel, two renowned experts in numerical analysis of differential equations, provide a compelling answer to this question. …”
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“…The differential equations of fluid flow are approximated by finite difference equations and these in turn are numerically integrated in a stepwise manner, with artificial viscosity introduced into the numerical calculations in order to deal with shocks. …”
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“…The results are in good agreement with the direct numerical integration. Applications are presented for particular structure designs.…”
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“…These scaling laws are then theoretically derived from the ray equations. Numerical integration of the ray equations also exhibit this behaviour—consistent with finite element numerical simulations as well as the theoretically derived scaling. …”
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“…Published data from inhalation studies involving accumulation and elimination of photocopy test toner, antimony trioxide, carbon black, and diesel exhaust particles were investigated. Numerical integration techniques were used to solve mass balance relationships based upon dust retention in a single lung compartment and clearance via an MM-like kinetic process. …”
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“…Electronic excitations of an electron bound to an alkali metal ion inside a droplet of superfluid (4)He are computed via a combination of helium density functional theory and the numerical integration of the Schrödinger equation for a single electron in a modified, He density dependent atomic pseudopotential. …”
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“…The analytic solution provides the substrate, enzyme, and microbial biomass concentration instantaneously and over all time domains without the use of numerical integration schemes or iterative solvers required to overcome transcendental functions. …”
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“…Subsequently, to deal with the entropy of complicated nonlinear function, two novel simulation algorithms are separately designed by combining the uniform discretization process and the numerical integration process with the proposed calculation formulas. …”
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“…While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. …”
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“…The framework of the MFM allows us to estimate magnetic entropy variation in a wide temperature range within the thermodynamics of the model and without using the usual numerical integration of Maxwell relation.…”
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“…Numerical results reveal that the beam shape coefficients calculated in this way can adequately describe a zero-order Bessel beam with insignificant difference when compared to other relative time-consuming methods involving numerical integration over the spherical coordinates of the GLMT coordinate system, or quadratures. …”
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“…Models are simulated either using stochastic simulation or numerical integration, and visualized in time and space. …”
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“…These results are corroborated by numerical integration of dynamical equations in real space. …”
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“…It is shown that the application of staggered grids in combination with explicit integration of the wave equation facilitates the decoupling of the solution and enables the application of a combination of implicit and explicit numerical integration techniques. The presented solution is applied to model the generation of ultrasound by a laser source in isotropic and transversely isotropic materials. …”
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“…METHODS AND MATERIALS: Using numerical integration methods, margins accounting for random errors and systematic errors were calculated for CTVs of different shapes and sizes. …”
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“…We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. …”
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“…Furthermore, as bridges in service are constantly vibrating because of passing vehicles, estimating the boundary conditions for the numerical integration is difficult. To address these problems, this paper proposes a method for determining the displacement of a bridge in service from its acceleration based on its free vibration. …”
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“…Specifically, we analyze three aspects of the models: (1) Using dynamical systems analysis, we demonstrate and explain the presence of direct current potentials in the simulated EEG that were previously undocumented. (2) We explain how the system was not ideally formulated for numerical integration of stochastic differential equations. …”
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“…These two distributions are suggested because numerical integration is not needed to evaluate the likelihood. …”
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