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Numerical analysis of a finite volume method for a 1-D wave equation with non smooth wave speed and localized Kelvin-Voigt damping
arXiv:2502.19947v3 Announce Type: replace-cross Abstract: In this paper, we study the numerical solution of an elastic/viscoelastic wave equation with non smooth wave speed and internal localized distributed Kelvin-Voigt damping acting faraway from the boundary. Our method is based on the Finite Volume Method (FVM) and we are interested in deriving the stability estimates and the convergence of the numerical solution to the continuous one. Numerical experiments are performed to confirm the...
Nonlinear numerical schemes using specular differentiation for initial value problems of first-order ordinary differential equations
arXiv:2601.09900v4 Announce Type: replace Abstract: This paper proposes specular differentiation in one-dimensional Euclidean space and provides its fundamental analysis, including a quasi-Fermat theorem and a quasi-Mean Value Theorem. As an application, this paper develops several numerical schemes for solving initial value problems for first-order ordinary differential equations. Based on numerical simulations, we select one scheme and prove its second-order consistency and convergence.
Novel approaches for the reliable and efficient numerical evaluation of Landau-type operators
arXiv:2402.02247v3 Announce Type: replace Abstract: Numerical approximations of Landau-type operators represent fundamental components of time integration methods for demanding problems such as inhomogeneous Vlasov-Landau-type equations. Substantial computational issues arise from the treatment of the physically most relevant three-dimensional case with Coulomb-type interaction. This work is concerned with the introduction and numerical comparison of novel approaches for the reliable and...
Novel approaches for the reliable and efficient numerical evaluation of Landau-type operators
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A machine-learning-assisted progressive digit-randomness screening framework for detecting non-random patterns in raw numerical research data
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Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEs
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Testing LLM Arithmetic Reasoning Generalization with Automatic Numeric-Remapping Attacks
arXiv:2606.03606v1 Announce Type: new Abstract: Large language models achieve strong performance on arithmetic reasoning benchmarks, and one common response to arithmetic brittleness is to delegate computation to code. Yet models are still often used in settings where they must reason directly from natural language, and trustworthy models should solve small-number arithmetic word problems without external tools. Prior work shows that LLMs are sensitive to numerical variation: a model may...
Testing LLM Arithmetic Reasoning Generalization with Automatic Numeric-Remapping Attacks
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Explicit numerical approximations for McKean-Vlasov stochastic differential equations in finite and infinite time
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Utility-Preserving De-Identification for Math Tutoring: Investigating Numeric Ambiguity in the MathEd-PII Benchmark Dataset
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