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Finite Fourier Series in Hyperbolic Initial-Boundary Value Problems for Domains with Curved Boundaries
AbstractThe Fourier method based on orthogonal splines is used to solve a linear hyperbolic initial-boundary value problem for a domain with a curved...
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Analogs of the Riesz Identity, and Sharp Inequalities for Derivatives and Differences of Splines in the Integral Metric
An analog of the Riesz interpolation formula is established. It allows us to obtain a sharp estimate for the first order derivative of a spline of...
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Equivalence of the Fundamental Spline and Green’s Function in Constructing an Exact Finite-Dimensional Analog of the Boundary-Value Problem for an Ordinary Differential Equation of the Fourth Order
The author considers a problem with the main and natural boundary conditions on an interval. A new method for constructing an exact discrete analog...
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Indefinite Abstract Splines with a Quadratic Constraint
We study an extension to Krein spaces of the abstract interpolating spline problem in Hilbert spaces, introduced by M. Atteia. This is a...
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Local Wavelet Adaptation of Cartesian Grids in Computational Fluid Dynamics
AbstractA method for dynamic local adaptation of graded Cartesian trees for the numerical solution of fluid dynamics problems is presented. Local...
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Spectral Analysis of Matrices in B-Spline Galerkin Methods for Riesz Fractional Equations
Polynomial B-spline collocation discretizations for Riesz fractional diffusion equations over uniform meshes have recently appeared in the literature...
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Spline: Variational Model in 3-D
By now, our finite-element mesh is quite regular and accurate. It is now time to define basis functions (B-splines) on it. What is a basis function?...
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An efficient fourth order Hermite spline collocation method for time fractional diffusion equation describing anomalous diffusion in two space variables
Anomalous diffusion of particles in fluids is better described by the fractional diffusion models. A robust hybrid numerical algorithm for a...
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Sinc integrals revisited
The purpose of this paper is the evaluation of the Fourier transform of powers of the sinc function multiplied by monomials, also in the cases when...
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Nonstationary Problems of Heat Conduction for a Thermosensitive Plate with Nonlinear Boundary Condition on One Surface
We propose a method for the determination of temperature fields formed in a plate with regard for the thermal radiation, temperature dependence of...
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Interactive Design of Cubic IPH Spline Curves
Indirect Pythagorean hodographs (IPH) spline curves are a set of curves which have rational Pythagorean hodographs after reparameterization by a...
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THB-Spline Approximations for Turbine Blade Design with Local B-Spline Approximations
We consider two-stage scattered data fitting with truncated hierarchical B-splines (THB-splines) for the adaptive reconstruction of industrial...
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\({\mathscr{L}}\)-Splines as Diffusive Limits of Dissipative Kinetic Models
Dissipative kinetic models inspired by neutron transport are studied in a (1 + 1)-dimensional context: first, in the two-stream approximation, then...
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On minimax cardinal spline interpolation
It is shown that in the problem of cardinal interpolation, spline interpolants of various degrees are R -minimax, with respect to corresponding...
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Nonparametric uncertain time series models: theory and application in brent crude oil spot price analysis
Uncertain time series models constitute a pivotal tool for analyzing phenomena evolving over time. However, most of the prevailing research centers...
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Coherent extrapolation of mortality rates at old ages applied to long term care
In an insurance context, Long-Term Care (LTC) products cover the risk of permanent loss of autonomy, which is defined by the impossibility or...
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Optimization of the Parameters of Feet and the Laws of Motion of Bipedal Walking Robots
We study the problem of joint optimization of the linear dimensions of feet and the laws of motion of bipedal walking robots. A robot is modeled as a...
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Sampling by Averages and Average Splines on Dirichlet Spaces and on Combinatorial Graphs
In the framework of a strictly local regular Dirichlet space X we introduce the subspaces PW ω, ω > 0, of Paley–Wiener functions of bandwidth ω. It...
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Modeling and Forecasting Natural Gas Futures Prices Dynamics: An Integrated Approach
We explore and test the capabilities of B-Splines and Dynamic De Rezende-Ferreira five–factor model to replicate the main dynamics and stylized facts...