Search Results - Advanced Numerical Methods in Computational Mathematics

An Eclectic View on Numerical Methods for PDEs: Presentation of the Special Issue “Advanced Numerical Methods: Recent Developments, Analysis and Applications” by Antonietti, Paola F., Droniou, Jérôme, Eymard, Robert

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Advanced Numerical and Computational Methods for Engineering and Applied Mathematical Problems

“… “Advanced Numerical and Computational Methods for Engineering and Applied Mathematical Problems…”
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A numerical study of mixed parabolic-gradient systems: Advanced Numerical Methods for Mathematical Modelling by VERWER, J. G, SOMMEIJER, B. P

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High-order convergent deferred correction schemes based on parameterized Runge-Kutta-Nyström methods for second-order boundary value problems: Advanced Numerical Methods for Mathematical Modelling by VAN HECKE, T, VAN DAELE, M

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Frequency determination and step-length control for exponentially-fitted Runge-Kutta methods: Advanced Numerical Methods for Mathematical Modelling by BERGHE, G. Vanden, IXARU, L. Gr, DE MEYER, H

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Advanced shifted first-kind Chebyshev collocation approach for solving the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel by Atta, A. G., Youssri, Y. H.

“…This research apparatuses an approximate spectral method for the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel (TFPIDE…”
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Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next by Cuomo, Salvatore, Di Cola, Vincenzo Schiano, Giampaolo, Fabio, Rozza, Gianluigi, Raissi, Maziar, Piccialli, Francesco

“…Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the…”
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Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations by Moseley, Ben, Markham, Andrew, Nissen-Meyer, Tarje

“… Compared to classical numerical methods, PINNs have several advantages, for example their ability to provide mesh-free solutions of differential equations and their ability to carry out forward…”
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Time-Fractional Allen–Cahn Equations: Analysis and Numerical Methods by Du, Qiang, Yang, Jiang, Zhou, Zhi

“…In this work, we consider a time-fractional Allen–Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional…”
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Intraday renewable electricity trading: advanced modeling and numerical optimal control by Glas, Silke, Kiesel, Rüdiger, Kolkmann, Sven, Kremer, Marcel, Graf von Luckner, Nikolaus, Ostmeier, Lars, Urban, Karsten, Weber, Christoph

“…As an extension of (Progress in industrial mathematics at ECMI 2018, pp. 469–475, 2019 ), this paper is concerned with a new mathematical model for intraday electricity trading involving both renewable and conventional generation…”
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Advanced Computational Modeling and Mechanical Behavior Analysis of Multi-Directional Functionally Graded Nanostructures: A Comprehensive Review by Gartia, Akash Kumar, Chakraverty, S.

“… distribution models like power-law, exponential, trigonometric, polynomial functions, etc. It also discusses the application of advanced size-dependent theories like…”
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Approximate solution of singular IVPs of Lane–Emden type and error estimation via advanced Adomian decomposition method by Umesh, Kumar, Manoj

“…This article aims to present a simple and effective method, named as advanced Adomian decomposition method, to attain the approximate solution of singular initial value problems of Lane–Emden type…”
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Effective methods for numerical analysis of the simplest chaotic circuit model with Atangana–Baleanu Caputo fractional derivative by Alzahrani, Abdulrahman B. M., Saadeh, Rania, Abdoon, Mohamed A., Elbadri, Mohamed, Berir, Mohammed, Qazza, Ahmad

“…This paper comprehensively studies effective numerical methods for solving the simplest chaotic circuit model…”
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Numerical methods for forward fractional Feynman–Kac equation by Nie, Daxin, Sun, Jing, Deng, Weihua

“… Hölder-type inequalities in Sobolev space to build the regularity of the solution, and then the fully discrete scheme constructed by convolution quadrature and finite element methods is developed…”
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Rank-Adaptive Tensor Methods for High-Dimensional Nonlinear PDEs by Dektor, Alec, Rodgers, Abram, Venturi, Daniele

“… The new method is designed to improve computational efficiency, accuracy and robustness in numerical integration of high-dimensional problems…”
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Global Convergence of ADMM in Nonconvex Nonsmooth Optimization by Wang, Yu, Yin, Wotao, Zeng, Jinshan

“…In this paper, we analyze the convergence of the alternating direction method of multipliers (ADMM…”
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Linear convergence of first order methods for non-strongly convex optimization by Necoara, I., Nesterov, Yu, Glineur, F.

“…The standard assumption for proving linear convergence of first order methods for smooth convex optimization is the strong convexity of the objective function, an assumption which does not hold…”
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Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems by Abgrall, R., Nordström, J., Öffner, P., Tokareva, S.

“…In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered…”
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A Second Order Accurate Scalar Auxiliary Variable (SAV) Numerical Method for the Square Phase Field Crystal Equation by Wang, Min, Huang, Qiumei, Wang, Cheng

“…In this paper we propose and analyze a second order accurate (in time) numerical scheme for the square phase field crystal equation, a gradient flow modeling crystal dynamics at the atomic scale in space but on diffusive scales in time…”
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Distributed stochastic gradient tracking methods by Pu, Shi, Nedić, Angelia

“… Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method (DSGT…”
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