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Quartic-trigonometric tension B-spline Galerkin method for the solution of the advection-diffusion equation
In this work, the numerical solutions of advection-diffusion equation are investigated through the finite element method. The quartic-trigonometric...
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Polynomial Optimization in Geometric Modeling
In this chapter, we review applications of Polynomial Optimization techniques to Geometric Modeling problems. We present examples of topical problems...
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Polynomial Approximation
This project is devoted to the approximation of a given real function defined on an interval...
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Directional wavelet packets originating from polynomial splines
The paper presents a versatile library of quasi-analytic complex-valued wavelet packets (qWPs) which originate from polynomial splines of arbitrary...
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Using a cubic B-spline method in conjunction with a one-step optimized hybrid block approach to solve nonlinear partial differential equations
In this paper, we develop an optimized hybrid block method which is combined with a modified cubic B-spline method, for solving non-linear partial...
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An Improved Extrapolated Collocation Technique for Singularly Perturbed Problems using Cubic B-Spline Functions
In this paper, an improved extrapolated collocation method with cubic B-spline as basis functions is presented. This method is applied to a class of...
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Solving Cardiac Bidomain Problems with B-spline Adaptive Collocation
B-spline collocation methods have been shown to be effective for solving systems of parabolic partial differential equations (PDEs). Using B-spline...
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Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto–Sivashinsky equation
A spline is a piecewise defined special function that is usually comprised of polynomials of a certain degree. These polynomials are supposed to...
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A new structure to n-dimensional trigonometric cubic B-spline functions for solving n-dimensional partial differential equations
In this paper, we present a new structure of the n -dimensional trigonometric cubic B-spline collocation algorithm, which we show in three different...
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Non-polynomial Cubic Spline Method for Three-Dimensional Wave Equation
The scientific community has always been showing deep concern towards partial differential equations (PDEs) and to approximate its numerical...
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Fitted operator method for parabolic singularly perturbed convection-diffusion problems via polynomial cubic spline
This article introduces a new fitted operator method for singularly perturbed parabolic convection-diffusion having right boundary layer. We...
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Generalized Polynomial Method for Solving a Cauchy-Type Problem for one Fractional Differential Equation
In this paper, we examine a Cauchy-type problem for one ordinary differential equation with Riemann–Liouville fractional derivatives. For this...
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Topologically Robust B-spline Reconstruction of Fibers from 3D Images
The micro-structure of wood-based insulation materials is analyzed to gain insight into how features on microscopic scales influence macroscopic...
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Solving Elliptic PDE’s Using Polynomial Splines on Curved Triangulations
It is shown how the polynomial splines defined on the curved triangulations introduced in our recent paper Larry L. Schumaker, A. Yu. (Comput. Aided...
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Polynomial Interpolation
Prior to describing the linear multistep method, another major class of numerical solution of ODEs, we will study interpolation, which is one of the...
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Fourth-order cubic B-spline collocation method for hyperbolic telegraph equation
In this article, a new method based on collocation of cubic B splines to find the numerical solution of one dimensional second-order hyperbolic...
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A second-order convergent nonconforming polynomial stokes element on quadrilateral meshes
In this paper, we construct a new mixed finite element for the Stokes problem on general convex quadrilateral partitions. The velocity is...
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An efficient cubic trigonometric B-spline collocation scheme for the time-fractional telegraph equation
In this paper, a proficient numerical technique for the time-fractional telegraph equation (TFTE) is proposed. The chief aim of this paper is to...
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On the Bertrand Pairs of Open Non-Uniform Rational B-Spline Curves
B-spline curves are used basically in Computer-Aided Design (CAD), Computer-Aided Geometric Design (CAGD), and Computer-Aided Modeling (CAM). In...
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Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms
In this work we extend some ideas about greedy algorithms, which are well-established tools for, e.g., kernel bases, and exponential-polynomial...