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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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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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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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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Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments by S. Shao, C. L. Chang

“…Based on the behavior of the total income flow, asymptotic and numerical methods are used to solve the special class of diffusion equations which govern the conditional ruin probability over finite time.…”
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Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients by Peng Jiang, Xiaofeng Ju, Dan Liu, Shaoqun Fan

“…The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.…”
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Image Restoration Based on the Hybrid Total-Variation-Type Model by Baoli Shi, Zhi-Feng Pang, Yu-Fei Yang

“…Since two L1-norm terms in the proposed model make it difficultly solved by using some classically numerical methods directly, we first employ the alternating direction method of multipliers (ADMM) to solve a general form of the proposed model. …”
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Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges by Wei Li, Chunrui Zhang, Mi Wang

“…This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. …”
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Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations by Sohrab Bazm, Fatemeh Pahlevani

“…This approach transforms the integral equation into a set of nonlinear algebraic equations, which can be efficiently solved by employing standard numerical methods like Newton's method or Picard iteration. …”
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Uniformly Convergent Nonpolynomial Spline Method for Singularly Perturbed Robin-Type Boundary Value Problems with Discontinuous Source Term by Habtamu Garoma Debela, Gemechis File Duressa

“…The numerical results are tabulated in terms of maximum absolute errors and rate of convergence, and it is observed that the present method is more accurate and ε-uniformly convergent for h≥ε where the classical numerical methods fail to give good result and it also improves the results of the methods existing in the literature.…”
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