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Journal of Numerical Analysis and Approximation Theory
Scopus
ISSN 2457-6794 · Publishing House of the Romanian Academy · 2.338 artikel di indeks
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Artikel Jurnal Teks lengkap
A new analytical envelope for multivariate global optimization
We propose a new global optimization method that combines an α–dense univariate reduction with explicitly constructed analytical envelopes: a piecewise concave underestimator (PCU) and a piecewise convex overestimator (PCO). By leveraging interval- based curvature bounds, the method provides…
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A defect-correction nodal finite element method for time-dependent Maxwell's equations on polygonal domains
This paper develops a nodal finite element Crank-Nicolson method of lines to solve the time-dependent Maxwell's equations on polygonal domains with reentrant corners. Nodal Finite Element methods are used to solve Maxwell's equations with an optimal convergence rate when the domain is convex or has…
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An Ushijima-type analysis for the numerical blow-up of a fractional reaction-diffusion equation
This paper is devoted to the rigorous analysis of the blow-up phenomenon for a nonlinear reaction-diffusion equation with a Caputo fractional time derivative. Our approach is twofold. First, we prove that the solution of a semi-discretized system blows up in a finite time Th under a suitable…
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On a generalization of the Stancu-Schurer operator of higher order
In this paper, we introduce a generalization of the higher-order Stancu–Schurer operator. Starting from a particular form of the operator recently introduced by the authors, we extend the convex combination of two terms appearing in its expression to a convex combination of $m$ functions, where…
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Dynamics of a model of nonlocal dispersion viral infection that includes humoral immunity, intracellular delay, and virus-to-cell and cell-to-cell transmissions
This paper investigates a delayed spatiotemporal viral infection model with two types of transmissions, namely, virus-to-cell transmission, and virus-to-cell transmission, and a special focus on the cell-mediated immunity. First, we establish that the model system has a global attractor and that…
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On the enhanced structures and rough paths integrals for time-changed paths
In this paper, we study the effects of a discontinuous time change \( \phi \) on a continuous path \( x \). While rough integration in this setting poses significant challenges, we construct an enhancement for the time-changed path \( x \circ \phi \), providing a structured framework for…
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Improving approximation via linear combinations of Bernstein operators
In this paper, a new way to improve approximation operators is proposed. Two well-known methods are combined: the linear combination of the classic Bernstein operator and the iteration technique. The main goal is to make the convergence to the function faster and to obtain more accurate numerical…
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Second-order polygonal discretization of the area functional and explicit error asymptotics
We study a geometric polygonal discretization of the area functional \[ A(\gamma) = \frac{1}{2} \int_a^b (x,dy - y,dx) \] for planar parametrized curves. The method is based on a chordal (shoelace-type) construction and depends only on endpoint values of the parametrization. We establish…
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Book reviews
Imre Boros: Peter M. Kogge, The Zen of Exotic Computing, SIAM, Philadelphia, 2023, XXXI + 386 pp., ISBN 978-1-61197-728-8 (paperback), eISBN 978-1-61197-729-5.
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On the coordinate system-dependence of the accuracy of symplectic numerical methods
Symplectic numerical methods have become a widely-used choice for the accurate simulation of Hamiltonian systems in various fields, including celestial mechanics, molecular dynamics and robotics. Even though their characteristics are well-understood mathematically, relatively little attention has…
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Modified adaptive quadrature by expansion for Laplace and Helmholtz layer potentials in 2D
An adaptive algorithm based on quadrature by expansion (QBX) is proposed for computing layer potentials at target points near or on a smooth boundary in \(\mathbb{R}^2\). The algorithm can be viewed as major modifications to the two-phase algorithm AQBX, proposed recently by Klinteberg et al. [SIAM…
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Reconstruction inversion formulas for the Laguerre Gabor transform
In this paper, we define and study the Gabor transform in the context of the Laguerre hypergroup. We prove some of its basic properties, such as Plancherel theorem, inversion formula and Calder´on’s reproducing inversion formula. Next, using the harmonic analysis related to Laguerre hypergroup, we…
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Two step Steffensen-type methods with or without memory for nondifferentiable equations
A wide range of applications emerging from diverse disciplines are formulated as an equation or system of equations in abstract spaces such as Euclidean multidimensional, Hilbert or Banach to mention a few, a plethora of which are nondifferentiable. Different methodologies are developed worldwide…
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ATM transaction simulation: combination of ACDs and cox process
Two main approaches for analyzing the ultra-frequency data such as ATM (auto teller machine) transaction are Cox process and autoregressive conditional durations (ACDs). This paper combines both models and proposes some simulated results. The functional data analysis proposes useful method for…
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Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena
In this work, a comprehensive analysis of a multi-step iterative composition for nonlinear equation is performed, providing insights into both local and semilocal convergence properties. The analysis covers a wide range of applications, elucidating the parameters affecting both local and semilocal…
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A numerical approach for singularly perturbed parabolic reaction-diffusion problem on a modified graded mesh
This paper addresses the numerical approximations of solutions for one dimensional parabolic singularly perturbed problems of reaction-diffusion type. The solution of this class of problems exhibit boundary layers on both sides of the domain. The proposed numerical method involves combining the…
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Lebesgue constants for Cantor sets. Numerical results
We analyze numerically the form of Lebesgue functions and the values of Lebesgue constants in polynomial interpolation for three types of Cantor sets.
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A comparative study on balanced truncation and projection onto the dominant eigenspace of the Gramian using Laguerre functions
This paper presents a comparative analysis of two model reduction techniques: balanced truncation and projection onto the dominant eigenspace of the Gramian. Both methods are evaluated through the lens of Laguerre functions which is a reduction technique based on Laguerre function expansion, that…
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