Formation of Temperature Mode in Internal Spaces of Armored Machinery by P. I. Dziachek, A. S. Mezentsev

“…An algorithm and a program  have been developed for calculation of temperature mode in a T-72 tank tower while using numerical methods. The paper reveals a satisfactory convergence of calculated and experimental data. …”
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Sensitivity Analysis of Wear on Metal-On-Metal Bearing Couples via Verification of Numeric and Analytic Methods by Alican Tuncay Alpkaya, Senay Mihcin

“…The results are compared to the numeric method’s results obtained from the finite element method. …”
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A leaky integrate-and-fire model with adaptation for the generation of a spike train by Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora

“…We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. …”
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Chaos Control and Synchronization in Fractional-Order Lorenz-Like System by Sachin Bhalekar

“…The chaotic behavior of the system is studied using analytic and numerical methods. The minimum effective dimension is identified for chaos to exist. …”
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Experimental and Computational Fluid Dynamics: decades of turbulent EFD/CFD complementarity by Bonnet, Jean Paul

“…The growing evidence of organized motions in turbulent flows pushes in parallel both experiments and numerical approaches to develop new measurement technologies and numerical methods. Many tools and concepts are shared both by experiments and computations. …”
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Discretization of a mathematical model for image analysis based on the optics of spiral beams by S.A. Kishkin, S.P. Kotova

“…The process of its discretization is discussed in more detail as part of the development of numerical methods that allow the proposed model to be implemented using modern computer technology, while achieving real-time performance. …”
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Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems by Min Wu, Zhengfeng Yang, Wang Lin

“…A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. …”
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Calculation of Wall Heat Conductivity under Non-Symmetric Boundary Conditions by R. I. Yesman

“…Solution of the problem has been realized by numerical methods in accordance with the developed algorithms.…”
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Multi-parameter crack tip stress state description for estimation of fracture process zone extent in silicate composite WST specimens by Václav Veselý, Jakub Sobek, Lucie Šestáková, Petr Frantík, Stanislav Seitl

“…For wedge splitting test specimens, the stress and displacement fields both in the vicinity and also in larger distance from the crack tip are investigated by means of numerical methods. Several variants of boundary conditions were modeled. …”
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Design of Blast-Loaded Glazing Windows and Facades: A Review of Essential Requirements towards Standardization by Martin Larcher, Michel Arrigoni, Chiara Bedon, J. C. A. M. van Doormaal, Christof Haberacker, Götz Hüsken, Oliver Millon, Arja Saarenheimo, George Solomos, Laurent Thamie, Georgios Valsamos, Andy Williams, Alexander Stolz

“…In recent years numerical methods have become much more powerful also with respect to this kind of application. …”
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Multi-parameter crack tip stress state description for estimation of fracture process zone extent in silicate composite WST specimens by Václav Veselý, Jakub Sobek, Lucie Šestáková, Petr Frantík, Stanislav Seitl

“…For wedge splitting test specimens, the stress and displacement fields both in the vicinity and also in larger distance from the crack tip are investigated by means of numerical methods. Several variants of boundary conditions were modeled. …”
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Taylor Expansion of Surface Potential in MOSFET: Application to Pao-Sah Integral by Hugues Murray, Patrick Martin, Serge Bardy

“…The solution is presented analytically wherever possible, and the integration is made from simple numerical methods (Simpson, Romberg) or adaptative algorithms and can be implemented in simple C-program or in usual mathematical software. …”
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A Fourth-Order Compact Finite Difference Scheme for Solving the Time Fractional Carbon Nanotubes Model by N. H. Sweilam, Khloud R. Khater, Zafer M. Asker, Waleed Abdel Kareem

“…In this work, we deal with unsteady magnetohydrodynamic allowed convection inflow of blood with a carbon nanotubes model; the single and multiwalled carbon nanotubes of human blood are used as a based fluid. Two numerical methods used to study this model are the weighted average finite difference method and the nonstandard compact finite difference method. …”
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Geometric Josephson junction by Fabiano F. Santos, Henrique Boschi-Filho

“…This approach lead us to analytical solutions rather than usual numerical methods. Our computations on the gravity side reproduce the standard relation between the current across the junction and the phase difference of the condensate controlled by the tension Σ. …”
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Analytical Solution of System of Volterra Integral Equations Using OHAM by Muhammad Akbar, Rashid Nawaz, Sumbal Ahsan, Dumitru Baleanu, Kottakkaran Sooppy Nisar

“…Moreover, OHAM does not require discretization like other numerical methods and is also free from small or large parameter.…”
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Complex Dynamics in Generalized Hénon Map by Meixiang Cai

“…Chaos in the sense of Marotto's definition is proved by analytical and numerical methods. The numerical simulations show the consistence with the theoretical analysis and reveal some new complex phenomena which can not be given by theoretical analysis, such as the invariant cycles which are irregular closed graphics, the six and forty-one coexisting invariant cycles, and the two, six, seven, nine, ten, and thirteen coexisting chaotic attractors, and some kinds of strange chaotic attractors.…”
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An Accurate Predictor-Corrector-Type Nonstandard Finite Difference Scheme for an SEIR Epidemic Model by Asma Farooqi, Riaz Ahmad, Rashada Farooqi, Sayer O. Alharbi, Dumitru Baleanu, Muhammad Rafiq, Ilyas Khan, M. O. Ahmad

“…Simulations are performed to guarantee the results, and its effectiveness is compared with well-known numerical methods such as Runge–Kutta (RK) and Euler method of a predictor-corrector type.…”
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Transosseous Tie Fixation Using Krackow Sutures and Bone Tunnels in a Comminuted Fracture of the Upper Pole of the Patella: A Case Report by Jong Seok Baik

“…Conventional methods such as tension-band wiring are not enough to gain proper fixation strength. Numerous methods have been reported, including circumferential cerclage wiring, osteosynthesis, and suture anchors depending on the fracture pattern. …”
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IMPROVED FINITE ELEMENT TRANSFER MATRIX METHOD OF PLANE BEAM ELEMENTS USING THE ABSOLUTE NODAL COORDINATE FORMULATION by QIAN ShuangLin, HE Bin, YAO LiKe, NI ChunHai, LV JianDong

“…Here ordinary differential equation numerical methods can be applied conveniently. Finally,the method is verified correct by an example,the beam with large overall motion and small deformation.…”
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Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term by Hengfei Ding, Changpin Li

“…The stability analysis of the derived numerical methods is given by means of the fractional Fourier method. …”
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