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Redefined quintic B-spline collocation technique for nonlinear higher order PDEs
The objective of this work is to present a redefined quintic B-spline (QB-spline) collocation technique for nonlinear higher order PDEs. Two types of...
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A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic B-spline functions
We present a collocation approach based on redefined cubic B-spline (RCBS) functions and finite difference formulation to study the approximate...
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Zipper rational fractal interpolation functions
A classical piecewise interpolant can be redefined by utilizing horizontal contractive maps that project the entire domain onto subintervals,...
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The numerical study of advection–diffusion equations by the fourth-order cubic B-spline collocation method
A fourth-order numerical method based on cubic B-spline functions has been proposed to solve a class of advection–diffusion equations. The proposed...
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Viscous Effect on Solitary Kelvin Wave in Open Cylindrical Channel under Precession
Viscous effect is introduced into the system of Navier–Stokes equations, that were derived to study the solitary Kelvin mode in an open cylindrical...
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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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Numerical dynamics of the Generalized Equal Width (GEW) wave equation in presence of high-order nonlinearity
In the present manuscript, Generalized Equal Width (GEW) wave equation which is an alternative model to shallow water wave with high-order...
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Numerical Stability and Convergence for Delay Space-Fractional Fisher Equations with Mixed Boundary Conditions in Two Dimensions
In this paper, for generalized two-dimensional delay space-fractional Fisher equations with mixed boundary conditions, we present the stability and...
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Application of CCC–Schoenberg operators on image resampling
Image resampling is a widely used tool in image processing. The upsampling increases the number of pixels and introduces new information to the image...
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Nonparametric Regression
This chapter introduces nonparametric regression for a single predictor variable, discusses the curse of dimensionality that plagues nonparametric...
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Transparent boundary conditions and numerical computation for singularly perturbed telegraph equation on unbounded domain
In this paper, we study the numerical solution for the singularly perturbed telegraph equation (SPTE) on unbounded domain. Firstly, we investigate...
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Finite-Element Methods
Finite-element methods provide more flexibility in approximating functions and domains. These advantages can be exploited for the pricing of options,...
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The Forward and Adjoint Methods of Global Electromagnetic Induction for CHAMP Magnetic Data
Detailed mathematical derivations of the forward and adjoint sensitivity methods are presented for computing the electromagnetic induction response...
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Finite-Element Methods
Finite element methods provide more flexibility in approximating functions and domains. These advantages can be exploited for the pricing of options,...
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Regression Trees and Adaptive Splines for a Continuous Response
The theme of this chapter is to model the relationship between a continuous response variable Y and a set of p predictors, x 1,…, x...
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The Forward and Adjoint Methods of Global Electromagnetic Induction forCHAMP Magnetic Data
Detailed mathematical derivations of the forward and adjoint sensitivity methods are presented for computing the electromagnetic induction response...
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Nonparametric Regression
In this volume, we study univariate nonparametric regression problems. The prototypical example is where one observes the data where ε...
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Topology optimization by distribution of isotropic material
In this chapter we present an overview of the basic ingredients of what we will denote as the material distribution method for finding the optimum...
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Nonlinear Hyperbolic Systems of Generalized Navier-Stokes Type for Interactive Motion in Biology
We review two modelling approaches to obtain genuinely nonlinear systems of one hyperbolic transport equation (for density) accompanied by parabolic...
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Nonparametric Regression
In the late 1990’s, the orthogonal series approach to nonparametric regression became increasingly popular; see Hart (1997), Ogden (1997), and...