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Multivariate spline and algebraic geometry

Journal of Computational and Applied Mathematics, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ren-Hong Wang
exaly   +4 more sources

The correspondence between multivariate spline ideals and piecewise algebraic varieties

Journal of Computational and Applied Mathematics, 2011
Let \(\Delta\) be the partition of a region in affine space into a finite number of polyhedral cells. A \textit{multivariate spline} with smoothness \(\mu\) over \(\Delta\) is a \(C^\mu\)-function whose restriction to each cell of \(\Delta\) is a polynomial.
Chun-Gang Zhu, Ren-Hong Wang
exaly   +4 more sources

On the Stability of the Spline-Collocation Difference Scheme for a Semilinear Differential-Algebraic Index System (1,0) [PDF]

Известия Иркутского государственного университета: Серия "Математика", 2018
In the paper, a semi-linear differential-algebraic system of partial differential equations of index (1, 0) with a rectangular domain of definition and compatible initial-boundary conditions is considered.
S. V. Svinina
doaj   +2 more sources

An algebraic spline model of molecular surfaces for energetic computations. [PDF]

IEEE/ACM Trans Comput Biol Bioinform, 2011
In this paper, we describe a new method to generate a smooth algebraic spline (AS) approximation of the molecular surface (MS) based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the Protein data bank (PDB).
Zhao W, Xu G, Bajaj C.
europepmc   +4 more sources

Spline-in-compression approximation of order of accuracy three (four) for second order non-linear IVPs on a graded mesh. [PDF]

MethodsX, 2023
A spline-in-compression method, implicit in nature, for computing numerical solution of second order nonlinear initial-value problems (IVPs) on a mesh not necessarily equidistant is discussed.
Mohanty RK, Ghosh BP.
europepmc   +2 more sources

A new technique for numerical solution of 1D and 2D non-linear coupled Burgers’ equations by using cubic Uniform Algebraic Trigonometric (UAT) tension B-spline based differential quadrature method

Ain Shams Engineering Journal, 2021
In present paper, a new technique is developed named Uniform Algebraic Trigonometric (UAT) tension B-spline based DQM, for the better numerical approximation of coupled 1D and coupled 2D Burgers’ equation.
Mamta Kapoor, Varun Joshi
exaly   +3 more sources

Cubic non-polynomial spline on piecewise mesh for singularly perturbed reaction differential equations with robin type boundary conditions. [PDF]

BMC Res Notes
Objective The main purpose of this work is to present cubic non-polynomial spline approximation method for solving Robin-type singularly perturbed reaction–diffusion problems. Results The solution domain is first discretized using a piecewise mesh.
Esayas Ayele B, Bullo TA, Duressa GF.
europepmc   +2 more sources

Convergence Analysis of Cubic Spline Function with Fractional Degree and Applications [PDF]

مجلة جامعة الانبار للعلوم الصرفة, 2023
In this paper, a fractional degree cubic spline scheme is proposed and analyzed for fractional order with the multi-term Riemann–Liouvile (R–L) derivatives. For the integral and fractional differential equations, we handle fractional continuity equations
Twana Hidayat, Faraidun Hamasalh, Mizhda Headayat   +2 more
doaj   +1 more source

Multivariate Splines and Algebraic Geometry [PDF]

Oberwolfach Reports, 2016
Multivariate splines are effective tools in numerical analysis and approximation theory. Despite an extensive literature on the subject, there remain open questions in finding their dimension, constructing local bases, and determining their approximation power. Much of what is currently known was developed by numerical analysts, using classical methods,
Tom Lyche, Henry Schenck, Tatyana Sorokina   +2 more
openaire   +1 more source

A comparative study for the numerical approximation of 1D and 2D hyperbolic telegraph equations with UAT and UAH tension B-spline DQM

Nonlinear Engineering, 2023
Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while the second implemented regime is uniform ...
Kapoor Mamta
doaj   +1 more source