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Numerical simulations of reaction–diffusion systems in biological and chemical mechanisms with quartic-trigonometric B-splines
This article concerns with the numerical investigations of the reaction–diffusion systems (RDSs) arising in the study of pattern formation in...
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An Adaptive Collocation Method with Weighted Extended PHT-Splines
This paper presents an adaptive collocation method with weighted extended PHT-splines. The authors modify the classification rules for basis...
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A Method for the Construction of LocalParabolic Splines with Additional Knots
We propose a general method for the construction of local parabolic splines with an arbitrary arrangement of knots for functions given on grid...
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THE STUDY BY SPLINES OF NORM INEQUALITIES FOR RIEMANN–LIOUVILLE OPERATORS IN WEIGHTED BESOV SPACES
The work is devoted to the study of boundedness properties of integration and differentiation operators of Riemann–Liouville type on the real axis...
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Stochastic Collocation with Hierarchical Extended B-Splines on Sparse Grids
B-spline approximations with uniform isotropic tensor product grids soon reach computational limits, because the grid size increases exponentially...
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On Maximally Oscillating Perfect Splines and Some of Their Extremal Properties
In this paper we study analogues of the perfect splines for weighted Sobolev classes of functions defined on the half-line. Maximally oscillating...
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Convergence of Quartic Interpolating Splines
The problem of interpolation by quartic splines according to Marsden’s scheme is considered. It is shown that the calculation of an interpolating...
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Correction to: Indefinite Abstract Splines with a Quadratic Constraint
A Correction to this paper has been published: 10.1007/s10957-020-01692-z
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Application of Cubic Splines on Bakhvalov Meshes in the Case of a Boundary Layer
AbstractThe problem of cubic spline interpolation on Bakhvalov meshes for functions with high gradients is considered. Error estimates are obtained...
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A collocation method based on cubic trigonometric B-splines for the numerical simulation of the time-fractional diffusion equation
Fractional differential equations sufficiently depict the nature in view of the symmetry properties, which portray physical and biological models. In...
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Superconvergent Methods Based on Cubic Splines for Solving Linear Integral Equations
In this paper we propose two collocation methods, based on superconvergent cubic spline interpolant and quasi-interpolant, for approximating the...
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Progressive Iterative Approximation for Extended Cubic Uniform B-Splines with Shape Parameters
In this paper, we concern with the data interpolation by using extended cubic uniform B-splines with shape parameters. Two iterative formats, namely...
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Discrete Splines and Its Applications
In this paper, we survey the contributions made to discrete splines in the literature and present some applications of discrete splines in the...
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Compass Construction of Bézier Curves and B-Splines
This article reveals a mathematical bridge between compass-only geometric constructions and parametric curves. A set of construction algorithms are...
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A Method for Solving the Fredholm Integral Equation of the First Kind
The paper considers a numerical method for solving the Fredholm integral equation of the first kind. The essence of the method is to replace the...