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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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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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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Modeling of Unsteady Flow through the Canals by Semiexact Method by Farshad Ehsani, Seyed Ghorban Hosseini, Hossein Soury

“…In this paper the Saint Venant equations and continuity equation are solved with homotopy perturbation method (HPM) and comparison by explicit forward finite difference method (FDM). …”
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The “Projection-by-Projection” (PbP) criterion for multiaxial random fatigue loadings by Denis Benasciutti, Davide Zanellati, Alessandro Cristofori

“…A first numerical example is then illustrated, in which various types of biaxial random stress are applied to three materials with different tension/torsion fatigue properties. Results of each analysis step are displayed explicitly to allow a plain understanding of how the PbP method works. …”
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Application of Homogenization Method in Free Vibration of Multi-Material Auxetic Metamaterials by Kadir Gunaydin, Orhan Gülcan, Aykut Tamer

“…However, due to the higher computational time spent on the modelling of lattice structures, different methods have been investigated to accurately predict mechanical properties. …”
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Numerical study on the influence of material heterogeneity on mode III crack propagation using a phase-field model by Alfat S., Eso R., Barata L. O. A., Rianse M. S.

“…In this study, we investigate the influence of material heterogeneity on mode III crack growth using a phase-field model. The phase-field method offers a powerful computational framework for simulating crack initiation, propagation, and branching without explicitly tracking the crack surface. …”
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Method of matched sections in application to thin-walled and Mindlin rectangular plates by Kirill Danylenko, Igor Orynyak

“… The paper elaborates the principally new variant of finite element method in application to plate problem. …”
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Two Numerical Methods for Solving the Schrödinger Parabolic and Pseudoparabolic Partial Differential Equations by Mahmut Modanli, Bushra Bajjah, Sevgi Kuşulay

“…The modified double Laplace decomposition method is applied to get the semianalytic solutions and the explicit finite difference method to get the approximate solutions of the problems. …”
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Simulation of Water Coning in Oil Reservoirs Using a Corrected IMPES Method

“…This method has no complexity compared to the fully implicit method, although both of them are based on the finite difference technique. …”
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Numerical schemes for 3D parabolic problem with non-local boundwy condition by Raimondas Čiegis, Mečislovas Meilūnas, Olga Subač

“… Two finite difference schemes are used to solve the 3D parabolic problem with a non-local boundary condition. …”
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A High Accuracy Local One-Dimensional Explicit Compact Scheme for the 2D Acoustic Wave Equation by Mengling Wu, Yunzhi Jiang, Yongbin Ge

“…Based on the local one-dimensional (LOD) method and Padé difference approximation, a fourth-order accuracy explicit compact difference scheme is proposed. …”
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Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing by R. Company, V. N. Egorova, L. Jódar

“…This paper presents an explicit finite-difference method for nonlinear partial differential equation appearing as a transformed Black-Scholes equation for American put option under logarithmic front fixing transformation. …”
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Stability analysis of a numerical method for the 3D high-order Allen–Cahn equation by Seokjun Ham, Jyoti, Jaeyong Choi, Yunjae Nam, Junseok Kim

“…We used a fully explicit Euler scheme for temporal derivatives and a second-order finite difference approach for spatial discretization. …”
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Bio-Inspired Thin-Walled Straight and Tapered Tubes with Variable Designs Subjected to Multiple Impact Angles for Building Constructions by Quanjin Ma, Nor Hazwani Mohd Yusof, Santosh Kumar Sahu, Yiheng Song, Nabilah Afiqah Mohd Radzuan, Bo Sun, Ahmad Yunus Nasution, Alagesan Praveen Kumar, Mohd Ruzaimi Mat Rejab

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Full-Wave Analysis of the Shielding Effectiveness of Thin Graphene Sheets with the 3D Unidirectionally Collocated HIE-FDTD Method by Arne Van Londersele, Daniël De Zutter, Dries Vande Ginste

“…Here, a unidirectionally collocated hybrid implicit-explicit (UCHIE) FDTD method is put forward that exploits the planar structure of graphene to increase the time step by implicitizing the critical dimension. …”
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Finite Element Simulation Analysis of Dynamic Contact Characteristic of Deep Groove Ball Bearing by Bai Guicai, Shentu Liufang

“…A multi-body dynamic contact finite element model of a deep groove ball bearings that be used in planetary gear is established in LS-DYNA,based on explicit dynamics finite element method,considering effect of rotational speed of bearing outer ring,radial load and rotational speed of carrier,the simulation analysis of dynamic contact characteristic（displacement,velocity,stress and contact force）under different working conditions are carried out,the dynamic contact response of the bearing is obtained.The study shows that the rolling exist revolution and rotation movement during operation,the maximum and the minimum line speed occurred at the contact point with the outer ring and the inner ring.The maximum stress occurred when the rolling contact with outer ring or inner ring,and the influence of the rotational speed to the maximum stress is little.It is proved reliable based on the simulation results compared with Hertz solution.The contacting force fluctuation between the rolling and cage is bigger than that and the inner or outer ring,but the value is the minimum,the contacting force value between the rolling and the outer ring or inner is almost same with the radial load.…”
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Numerical Simulation of Finite Deformations of a Dynamically Loaded Elasto-Viscoplastic Circular Membrane by W. Dornowski

“…The theory is completed by an algorithm of the explicit finite difference method. With respect to the conditional stability of that method, the stability criterion is given. …”
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An exact implementation of the generalized Zhang-Zhu criterion for elasto-plastic finite element calculations by Lianjin Tao, Linkun Huang, Xu Zhao, Johan Clausen, Qi Zhang, Boyang Jiao, Hehua Zhu

“…The return mapping is employed to compute the updated stress and consistent stiffness matrix, facilitating calculations using both finite element implicit and explicit algorithms. Finally, the accuracy of the proposed method is validated using rock true triaxial test data and semi-analytical solutions for stresses and displacement around a circular opening under the GZZ criterion.…”
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Finite mixtures of functional graphical models: Uncovering heterogeneous dependencies in high-dimensional data. by Qihai Liu, Kevin H Lee, Hyun Bin Kang

“…Graphical models have been widely used to explicitly capture the statistical relationships among the variables of interest in the form of a graph. …”
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