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High-Order Splines on Riemannian Manifolds
AbstractThis paper is an overview of the work of the authors about generalized polynomial curves and splines on Riemannian manifolds. The emphasis...
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A convergent exponential B-spline collocation method for a time-fractional telegraph equation
This work aims to develop and analyze a numerical method for solving a time-fractional telegraph equation of Caputo type. The method is constructed...
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Second-Order Semi-Lagrangian Exponential Time Differencing Method with Enhanced Error Estimate for the Convective Allen–Cahn Equation
The convective Allen–Cahn (CAC) equation has been widely used for simulating multiphase flows of incompressible fluids, which contains an extra...
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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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Error Analysis Through Energy Minimization and Stability Properties of Exponential Integrators
In this article, the stability property and the error analysis of higher-order exponential variational integration are examined and discussed. Toward...
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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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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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An exponential spline approximation for fractional Bagley–Torvik equation
In this paper, we approximate the solution of fractional Bagley–Torvik equation by using the exponential spline function and the shifted Grünwald...
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Euler Elasticas for Optimal Control of the Motion of Mobile Wheeled Robots: the Problem of Experimental Realization
This paper is concerned with the problem of optimal path planning for a mobile wheeled robot. Euler elasticas, which ensure minimization of control...
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Many-Stage Optimal Stabilized Runge–Kutta Methods for Hyperbolic Partial Differential Equations
A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge–Kutta methods is devised. Intended for...
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New alternative numerical approaches for solving the glioma model and their efficiencies
In this article, the numerical solution of glioma, or glioblastomas, which is one of the most aggressive forms of cancer is considered. A...
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Construction of Optimal Quadrature Formulas Exact for Exponentional-trigonometric Functions by Sobolev’s Method
The paper studies Sard’s problem on construction of optimal quadrature formulas in the space W
2 ( m ,0) by Sobolev’s method. This problem consists of... -
Stochastic Natural Frequencies of Functionally Graded Plates Based on Power Law Index
The present paper deals with the stochastic natural frequency analysis of functionally graded material (FGM) plates by employing the multivariate...
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Analog of the Riesz Identity and Sharp Inequalities for Derivatives and Differences of Splines in the Uniform Metric
We establish an analog of the Riesz interpolation formula owing to which it is possible to obtain a sharp estimate for the first order derivative of...