The Ultimate Bearing Capacity analysis of masonry arch bridges by Kefan Chen, Yuan Li, Qixiang Hui, Bin Zhou, Kang Wang

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Matrix Method of Defect Analysis for Structures with Areas of Considerable Stiffness Differences by Monika Mackiewicz, Tadeusz Chyży

“…The paper presents an innovative matrix method for defect analysis in heterogeneous structures with significant differences in stiffness parameters. …”
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Homogeneous difference schemes for the coupled problems of hydrodynamics and elasticity by I.P. Tsygvintsev, A.Yu. Krukovskiy, Yu.A. Poveshchenko, V.A. Gasilov, D.S. Boykov, S.B. Popov

“…Finite-difference approximations of elastic forces on the staggered moving grid were constructed. …”
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Comparative Study of Different Linear Analysis for Seismic Resistance of Buildings According to Eurocode 8 by Ivelin Ivanov, Dimitar Velchev

“…Using an artificial diagram, three approaches in finite element methods exist: explicit time integration, implicit time integration, and modal dynamics. …”
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An Advection Scheme using Paired Explicit Runge-Kutta Time Integration for Atmospheric Modeling by Zhaoyang SUN, Chungang CHEN, Xingliang LI, Xueshun SHEN

“…In this paper， a new numerical scheme was proposed to solve the advection equation in a multi-moment nonhydrostatic dynamical core.To guarantee the shape-preserving property， the limiting operations are devised for a hybrid discretization framework adopted by the multi-moment dynamical core， consisting of the multi-moment finite-volume and the conservative finite-difference schemes for the horizontal and vertical discretizations respectively.In the horizontal direction， a nonoscillaory scheme is accomplished by adjusting the slope of the multi-moment reconstruction polynomial at the cell center with the application of a WENO （weighted essentially non-oscillatory） algorithm.The resulting multi-moment scheme can achieve the fourth-order accuracy in the convergence test.In the vertical direction， a TVD （total variation diminishing） slope limiter is applied in the finite-difference discretization to remove the non-physical oscillations around the discontinuities.To accomplish the time marching in the proposed advection model， a second-order paired explicit Runge-Kutta scheme is adopted， which is expected to be an efficient and practical method for the advection solvers in the atmospheric models with very high spatial resolutions.The explicit time marching， without the dimension splitting， is useful to avoid the divergence errors in the advection transport calculations.Two Runge-Kutta schemes， requiring different times of conducting the spatial discretization within a time step， are combined， and used for the time marching in the different directions.The finite-difference discretization is called for six times within a time step in order to increase the maximum available CFL （Courant-Friedrichs-Lewy） number in the vertical direction， while the horizontal multi-moment spatial discretization is conducted for two times as the regular second-order schemes.As a result， the difference between the maximum time steps determined by the horizontal and vertical discretizations， due to the very large aspect ratio of the computational cells in atmospheric modeling， can be diminished.The non-negativity property of the proposed advection scheme is assured by devising a new flux-correction algorithm.It improves the existing positivity-preserving algorithm through further considering the mass flowing into the computational cell in an iterative procedure during the flux-correction operations.The proposed flux-correction algorithm can approach the necessary and sufficient condition for assuring the non-negative solutions and is more accurate for the advection calculations with CFL numbers larger than one.The widely used two-dimensional benchmark tests were checked in this study and the numerical results verified the performance the proposed advection scheme， which has the practical potential to build an accurate and efficient advection equation solver for the scalable high-resolution nonhydrostatic atmospheric models.…”
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A Second-Order Uniformly Stable Explicit Asymmetric Discretization Method for One-Dimensional Fractional Diffusion Equations by Lin Zhu

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Numerical Investigation of the Wave Equation for the Convergence and Stability Analysis of Vibrating Strings by Md Joni Alam, Ahmed Ramady, M. S. Abbas, K. El-Rashidy, Md Tauhedul Azam, M. Mamun Miah

“…The modeling of the one-dimensional wave equation is the fundamental model for characterizing the behavior of vibrating strings in different physical systems. In this work, we investigate numerical solutions for the one-dimensional wave equation employing both explicit and implicit finite difference schemes. …”
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Hybrid Finite Differences Technique for Solving the Nonlinear Fractional Korteweg-De Vries-Burger Equation by almutasim Hamed, Ekhlass Al-Rawi

“…Using a test problem to asses the HEFD method accuracy against the exact solution and the conventional explicit finite difference (EFD) method. …”
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The Analysis of Curved Beam Using B-Spline Wavelet on Interval Finite Element Method by Zhibo Yang, Xuefeng Chen, Yumin He, Zhengjia He, Jie Zhang

“…Instead of the traditional polynomial interpolation, scaling functions at a certain scale have been adopted to form the shape functions and construct wavelet-based elements. Different from the process of the direct wavelet addition in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space by aid of the corresponding transformation matrix. …”
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Numerical Simulation of Single-Phase Fluid Flow in Fractured Porous Media by M.V. Vasilyeva, V.I. Vasilyev, A.A. Krasnikov, D.Ya. Nikiforov

“…Approximation of the problem has been performed using the method of finite differences and the method of finite elements. …”
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Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System by Israa Th. Younis, Ekhlass S. Al-Rawi

“…Numerical results are obtained by comparing the exact solution with absolute and mean square errors using a test problem to assess the EFD-AP accuracy against the exact solution and the conventional explicit finite difference (EFD) method. The results exhibit excellent agreement between the approximate and exact solutions at different time values, and the results showed that the proposed EFD-AP method achieves superior accuracy and efficiency compared to the EFD method, which makes it a promising method for solving nonlinear partial differential systems of higher order.…”
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Breather and solitonic behavior of parametric Sine–Gordon equation with phase-shift and driven term by Taj Munir, Muhammad Zaman, Can Kang, Hussan Zeb, Alrazi Abdeljabbar, Mohammed Daher Albalwi

“…Analytically, a perturbative expansion combined with multiple-scale analysis is developed to derive system dynamics up to the fifth-order expansion. Numerically, the explicit finite difference scheme and the fourth-order Runge–Kutta finite difference method are implemented. …”
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Lateral stability analysis of steel tapered thin-walled beams under various boundary conditions by M. Soltani, S. Asil Gharebaghi, F. Mohri

“…Finite difference method, especially in its explicit formulation, is an extremely fast numerical method. …”
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Time-history simulation of civil architecture earthquake disaster relief- based on the three-dimensional dynamic finite element method by Liu Bing, Qi Yaoguang, Du Jiyun

“…Therefore, this paper develops a civil building earthquake disaster three-dimensional dynamic finite element numerical simulation system. The system adopts the explicit central difference method. …”
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POD-DEIM Based Model Order Reduction for the Spherical Shallow Water Equations with Turkel-Zwas Finite Difference Discretization by Pengfei Zhao, Cai Liu, Xuan Feng

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Parallel Jacobian Computation Based on Distance-2 Algorithm and Its Application in Coupling Problems by LIU Lixun, ZHANG Han, PENG Xinru, DOU Qinrong, WU Yingjie, GUO Jiong, LI Fu

“…How to calculate the Jacobian matrix efficiently and automatically is a major challenge. The finite difference method is an effective way to compute the Jacobian matrix automatically and can avoid the derivation of matrix element expressions. …”

TECHNICAL IMPLEMENTATION OF DISTRIBUTED CONTROLLERS by Sergey Dmitrievich Lomkov

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Explicit block encodings of boundary value problems for many-body elliptic operators by Tyler Kharazi, Ahmad M. Alkadri, Jin-Peng Liu, Kranthi K. Mandadapu, K. Birgitta Whaley

“…When restricted to rectangular domains with separable boundary conditions, we provide explicit circuits to block encode the many-body Laplacian with separable periodic, Dirichlet, Neumann, and Robin boundary conditions, using standard discretization techniques from low-order finite difference methods. …”
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Approximate Solution of Sub diffusion Bio heat Transfer Equation by Jagdish Sonawane, Bahusaheb Sontakke, Kalyanrao Takale

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A novel explicit scheme for stochastic diffusive SIS models with treatment effects by Muhammad Shoaib Arif

“…The scheme is designed as an explicit two-stage method, where only the time-dependent terms are discretized, ensuring computational efficiency. …”
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