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\(C^1\) -Rational Quadratic Trigonometric Spline Fractal Interpolation Functions
Trigonometric interpolation has an essential role in geometric modeling of conic data. In this paper, a novel...
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Adaptive Finite Element Thin-Plate Spline With Different Data Distributions
The thin-plate spline is a data fitting technique that possesses many favourable properties like insensitivity to noise [6]. One obstacle of its...
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B-Spline Collocation Discretizations of Caputo and Riemann-Liouville Derivatives: A Matrix Comparison
Two of the most famous definitions of fractional derivatives are the Riemann-Liouville and the Caputo ones. In principle, these formulations are not...
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Dimensions of Tri-Quadratic \( C^1 \) Spline Spaces over Hierarchical 3D T-meshes
A 3D T-mesh is generally a cuboid grid which allows hanging vertices. Here, a hanging vertex is an interior vertex, but it is not a corner point of...
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Approximate Solution of Nonlinear Differential Equations with the Help of Rational Spline Functions
AbstractA method for constructing an approximate solution in the form of a rational spline function is proposed for initial value problems in the...
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Scattered Data Approximation by LR B-Spline Surfaces: A Study on Refinement Strategies for Efficient Approximation
Locally refined B-spline (LRB) surfaces provide a representation that is well suited to scattered data approximation. When a data set has local...
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Periodic Orthonormal Spline Systems with Arbitrary Knots as Bases in \(\boldsymbol{H}^{\mathbf{1}}\boldsymbol{(\mathbb{T})}\)
AbstractWe give a simple geometric characterization of sequences of knots for which the corresponding periodic orthonormal spline system of order
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On Filter Banks in Spline Wavelet Transform on a Nonuniform Grid
AbstractAn explicit representation of filter banks is obtained for constructing wavelet transforms of spaces of linear minimal splines on nonuniform...
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Error analysis of Chebyshev polynomial-based numerical method for system of hypersingular integral equations
A system of hypersingular integral equations gets formed while solving curved crack or multi-crack problems in fracture mechanics. However, the issue...
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Spline Representations of Lizorkin–Triebel Spaces with General Weights
In this paper we introduce some new Lizorkin–Triebel type spaces of variable smoothness. Here the smoothness lies in a new weighted class. We give...
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Properties of Spline Spaces Over Structured Hierarchical Box Partitions
Given a spline space spanned by Truncated Hierarchical B-splines (THB), it is always possible to construct a spline space spanned by Locally Refined...
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De Boor–Fix functionals and Hermite boundary conditions in the polynomial spline interpolation problem
By means of de Boor–Fix functionals Hermite boundary conditions in the problem of spline interpolation are obtained. It is shown that some of the...
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Fourth-Order Numerical Scheme Based on Half-Step Non-Polynomial Spline Approximations for 1D Quasi-Linear Parabolic Equations
ABSTRACTIn this article, we discuss a fourth-order accurate scheme based on non-polynomial splines in tension approximations for solving quasi-linear...
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Cubic Spline on a Bakhvalov Mesh in the Presence of a Boundary Layer
The problem of cubic spline interpolation on the Bakhvalov mesh of functions with region of large gradients is considered. Asymptotically accurate...
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Matrix Representation of Filter Banks Corresponding to Spline Wavelets with Shifted Supports
The paper presents a matrix representation of filter banks corresponding to spline wavelets with shifted supports. The matrix form of the...
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Richardson Extrapolation of Nyström Method Associated with a Sextic Spline Quasi-Interpolant
In this paper, we analyse the Nyström method based on a sextic spline quasi-interpolant for approximating the solution of a linear Fredholm integral...
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A coupled scheme based on uniform algebraic trigonometric tension B-spline and a hybrid block method for Camassa-Holm and Degasperis-Procesi equations
In this article, high temporal and spatial resolution schemes are combined to solve the Camassa-Holm and Degasperis-Procesi equations. The...
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Nonpolynomial twin parameter spline approach to treat boundary-value problems arising in engineering problems
This study puts forward construction of an efficient nonpolynomial twin parameter cubic spline-based numerical scheme for approximations to the...
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Weight calculation and convergence analysis of polyharmonic spline (PHS) with polynomials for different stencils
Recent developments in the field of the radial basis function-finite difference (RBF-FD) framework have been focused on conditionally positive...
