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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7-DOF NONLINEAR VIBRATION ANALYSIS OF SHEARER UNDER CONDITION EXCITATION by CHEN HongYue, BAI YangXi, MAO Jun, SONG QiuShuang

“…Vibration characteristics of shearer under different traction speed was solved by numerical methods. The results show that the increasing of speed have great influence on the vibration displacement of back-end drum,have little effect on the fuselage,and have significant influence on Y axis vibration angle of the fuselage.…”
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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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Integrated correlators with a Wilson line in a N $$ \mathcal{N} $$ = 2 quiver gauge theory at strong coupling by Alessandro Pini

“…Finally, through a combination of analytical and numerical methods, we determine the leading terms of the corresponding strong-coupling expansions.…”
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GridLAB-D: An Agent-Based Simulation Framework for Smart Grids by David P. Chassin, Jason C. Fuller, Ned Djilali

“…This paper presents the numerical methods and approach to time-series simulation used by GridLAB-D and reviews applications in power system studies, market design, building control system design, and integration of wind power in a smart grid.…”
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Numerical Absorbing Boundary Conditions Based on a Damped Wave Equation for Pseudospectral Time-Domain Acoustic Simulations by Carlos Spa, Pedro Reche-López, Erwin Hernández

“…In the context of wave-like phenomena, Fourier pseudospectral time-domain (PSTD) algorithms are some of the most efficient time-domain numerical methods for engineering applications. One important drawback of these methods is the so-called Gibbs phenomenon. …”
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Emergency Gate Vibration of the Pipe-Turbine Model by Andrej Predin, Roman Klasinc

“…In particular the behavior is examined of the emergency gate for the case when the power unit is disconnected from the system or there is a breakdown of the guide vane system at the moment when the maximal head and capacity are achieved. Experimental-numerical methods both in the time domain and in the frequency domain are employed. …”
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Adaptive Optimal 𝑚-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems by Jui-Ling Yu

“…We present a class of numerical methods for the reaction-diffusion-chemotaxis system which is significant for biological and chemistry pattern formation problems. …”
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Using Resin Infiltration Technique and Direct Composite Restorations for the Treatment of Carious Lesions with Different Depths by İsmail Serhat Sadıkoğlu

“…Minimally invasive treatment methods are of special interest in restorative dental practice, with numerous methods emerging in the last decade. Such methods are being developed to encompass various applications, an important one being the detection and treatment of caries in the early stages. …”
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Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi by Ali Özyapıcı, Zehra B. Sensoy, Tolgay Karanfiller

“…In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. …”
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Two-step ranging based on energy detection for IR-UWB sensor networks by ZHANG Ting-ting1, ZHANG Qin-yu2, ZHANG Nai-tong1

“…A mathematical error model was set up for the two-step method which was veri-fied by the simulation results, and system parameters that affected the performance were studied by analytical and numerical methods. The results, compared with traditional ranging methods, show that this method achieves relative high performance under low complexity conditions.…”
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Simulation of Chloride Ingress through Surface-Coated Concrete during Migration Test Using Finite-Difference and Finite-Element Method by Seyoon Yoon

“…This paper presents the simulation of the effects of the surface coatings on migration tests by solving the Nernst-Planck/Poisson model using both finite-difference method and finite-element method. These two numerical methods were compared in terms of their accuracy and computational speed. …”
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Particle Concentration Comparison of Radiator and Floor Heating Systems under Zero Air Change Rate Condition by Mustafa Mutlu

“…Two different heating systems (radiator and floor heating systems) widely used in residential applications were compared for a room where the air change rate is zero, using numerical methods in terms of particle concentrations. 3D dimensional CFD simulations show that the floor heating system performs better in removing the pollutants dispersed homogeneously in the room, while the radiator system is more effective in removing the pollutants emitted from a source close to the floor. …”
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An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems by Chichia Chiu, Jui-Ling Yu

“…Theorems about stability and convergence of thealgorithm are given to show that the algorithm is highly stable and efficient.Numerical experiment results on a model problem are given for comparisonwith other numerical methods. Simulations on two real biological experimentswill also be shown.…”
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Stochastic Neutron Population with Temperature Feedback Effects Using the Implicit Runge-Kutta Scheme by Daniel Suescún-Díaz

“…The numerical simulations present good approximations in terms of means and standard deviations in agreement with other results using different numerical methods. The proposed scheme has good accuracy, it can be considered as an alternative method to simulate the time evolution of the stochastic density of the neutron population and the concentration of delayed neutron precursors considering temperature feedback effects.…”
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Improving the efficiency of adsorption filters with a short diffuser by improving their flow part by A. S. Korneeva, N. Yu. Filkin

“…The design process of the flow path of such filters is considered, which includes the stages of determining the parameters of the adsorbent layer, modeling gas-dynamic processes using numerical methods in the ANSYS CFX program and analyzing the results. …”
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