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An innovative fourth-order numerical scheme with error analysis for Lane-Emden-Fowler type systems
In this paper, we develop a novel higher-order compact finite difference scheme for solving systems of Lane-Emden-Fowler type equations. Our method...
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A robust second-order low-rank BUG integrator based on the midpoint rule
Dynamical low-rank approximation has become a valuable tool to perform an on-the-fly model order reduction for prohibitively large matrix...
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Unconditional energy stability and maximum principle preserving scheme for the Allen-Cahn equation
In this paper, we propose a novel fully implicit numerical scheme that satisfies both nonlinear energy stability and maximum principle for the space...
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Exploring the potential of Easy Language for enhancing website sustainability
Sustainable design principles have become increasingly important in website development, mainly focusing on reducing carbon emissions and energy...
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Weak convergence of tamed exponential integrators for stochastic differential equations
We prove weak convergence of order one for a class of exponential based integrators for SDEs with non-globally Lipschitz drift. Our analysis covers...
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Fractional Legendre wavelet approach resolving multi-scale optimal control problems involving Caputo-Fabrizio derivative
This article provides an effective numerical approach using the fractional integral operational matrix method for a fractional Legendre wavelet to...
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Unconditionally positivity-preserving approximations of the Aït-Sahalia type model: Explicit Milstein-type schemes
The present article aims to design and analyze efficient first-order strong schemes for a generalized Aït-Sahalia type model arising in mathematical...
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MyBioethics: How Ed-Tech Enables Discovery-Driven Empirical Bioethics Research
Digital tools have granted new opportunities to engage people with bioethical discussion and rehearsed decision-making. The ongoing development of...
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Error analysis of a high-order fully discrete method for two-dimensional time-fractional convection-diffusion equations exhibiting weak initial singularity
This study presents a novel high-order numerical method designed for solving the two-dimensional time-fractional convection-diffusion (TFCD)...
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Construction of high order numerical methods for solving fourth order nonlinear boundary value problems
In this paper, we construct numerical methods of fourth, sixth and eighth orders convergence for solving fully fourth order nonlinear differential...
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An Uzawa-DOS method for solving saddle-point problems
Based on the diagonal and off-diagonal splitting (DOS) iteration scheme (Dehghan et al. Filomat 31 (5), 1441–1452
2017 ), we offer an iteration... -
AI Ethics, the Neuralink Enigma, and Statistical Inference as the Anticlimax of Machiavelli’s Prince
Elon Musk’s Neuralink, one more company hopes to dominate the brain-computer interface (BCI) market, has implanted a brain-reading device into a...
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Inertial randomized Kaczmarz algorithms for solving coherent linear systems
In this paper, by regarding the two-subspace Kaczmarz method as an alternated inertial randomized Kaczmarz algorithm we present a better convergence...
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Optimal convergence analysis of the virtual element methods for viscoelastic wave equations with variable coefficients on polygonal meshes
The objective of this work is to develop a conforming virtual element method for viscoelastic wave equations with variable coefficients on polygonal...
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Caputo fractional derivative of \(\alpha \)-fractal spline
The Caputo fractional derivative of a real continuous function g distinguishes from the other fractional derivative methods with the demand for the...
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A new splitting mixed finite element analysis of the viscoelastic wave equation
This paper aims to propose a new splitting mixed finite element method (MFE) for solving viscoelastic wave equations and give convergence analysis....
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On the convergence of Galerkin methods for auto-convolution Volterra integro-differential equations
The Galerkin method is proposed for initial value problem of auto-convolution Volterra integro-differential equation (AVIDE). The solvability of the...
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An hp-version of the discontinuous Galerkin method for fractional integro-differential equations with weakly singular kernels
This paper suggests an hp -discontinuous Galerkin approach for the fractional integro-differential equations with weakly singular kernels. The key...
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Digital Health Empowerment, Autonomy, and the Capability Approach: Reply to de Proost and Grey
De Proost & Grey criticize Nickel et al.’s article “Justice and empowerment through digital health: ethical challenges and opportunities,” arguing...
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Safety and Privacy in Immersive Extended Reality: An Analysis and Policy Recommendations
Extended reality (XR) technologies have experienced cycles of development—“summers” and “winters”—for decades, but their overall trajectory is one of...