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A computational method for nonlinear Burgers’ equation using quartic-trigonometric tension B-splines
This work proposes a finite element method emphasizing with quartic-trigonometric basis functions for finding the numerical solution of nonlinear...
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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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Closed-form solution of a class of generalized cubic B-splines
Using the Blossom method in the quasi extended Chebyshev space, we first construct a class of generalized cubic Bernstein functions in the...
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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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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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Stabilization of spline bases by extension
We present a method to stabilize bases with local supports by means of extension. It generalizes the known approach for tensor product B-splines to a...
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Numerical simulations of Kuramoto–Sivashinsky equation in reaction-diffusion via Galerkin method
Finite element methods have been frequently employed in seeking the numerical solutions of PDEs. In this study, a Galerkin finite element numerical...
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Hermite interpolation by planar cubic-like ATPH
This paper deals with the construction of the Algebraic Trigonometric Pythagorean Hodograph (ATPH) cubic-like Hermite interpolant. A characterization...
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Positivity Preserving Rational Quartic Spline Zipper Fractal Interpolation Functions
In this paper, we introduce a class of novel \(C^1\)...
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A numerical algorithm for solitary wave solutions of the GEW equation
The present article attempts to obtain numerical solutions for the GEW equation with the Lie–Trotter splitting algorithm. For this reason, in...
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Construction of Trigonometric Box Splines and the Associated Non-Stationary Subdivision Schemes
In this paper, we define trigonometric box splines on regular triangular meshes using directional convolution. Using the theory, a non-stationary...
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Geometrically continuous piecewise Chebyshevian NU(R)BS
By piecewise Chebyshevian splines we mean splines with pieces taken from different Extended Chebyshev spaces all of the same dimension, and with...
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Symbolic Treatment of Trigonometric Parametrizations: The General Unirational Case and Applications
In this paper, we consider symbolic (hybrid trigonometric) parametrizations defined as tuples of real rational expressions involving circular and...
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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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Numerical Solution of Coupled Korteweg-de Vries Equation Employing Quintic Hyperbolic B-Spline Based Differential Quadrature Method
In the present paper, the differential quadrature method is functionalized to solve coupled Korteweg-de Vries equation numerically with the usage of...
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Integration of the RLW equation using higher-order predictor–corrector scheme and quintic B-spline collocation method
Solitary wave solutions are studied by way of the regularized long wave (RLW) equation. RLW equation is fully integrated by using combination of the...
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An Adaptive Element-Free Galerkin Approach for Solving Singularly Perturbed Boundary Layer Problems
AbstractThe paper’s objective is to propose a robust and dynamic mesh-free numerical approach to solve singularly perturbed problems(SPPs). As is...
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A new energy conservative scheme for regularized long wave equation
An energy conservative scheme is proposed for the regularized long wave (RLW) equation. The integral method with variational limit is used to...