Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments

Başhan, Ali

doi:10.1016/j.apnum.2021.05.015

Cited by 12 publications

(1 citation statement)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The work in [9] presents an improvement in some numerical methods to find the non-polynomial fractional spline, aiming to solve the fractional Korteweg-de Vries (KdV) equation with respect to time, as well as similar problems in various scientific fields, such as plasma physics and mechanics. Meanwhile, in [10], the quintic B-spline differential quadrature method is modified. This then implies that the algebraic system obtained does not have abstract points.…”

Section: Introductionmentioning

confidence: 99%

A Shape-Preserving Variational Spline Approximation Problem for Hole Filling in Generalized Offset Surfaces

Kouibia,

Pasadas,

Omri

2024

Mathematics

View full text Add to dashboard Cite

In the study of some real cases, it is possible to encounter well-defined geometric conditions, of an industrial or design type—for example, the case of a specific volume within each of several holes. In most of these cases, it is recommended to fulfil a function defined in a domain in which information is missing in one or more sub-domains (holes) of the global set, where the function data are not known. The problem of filling holes or completing a surface in three dimensions appears in many fields of computing, such as computer-aided geometric design (CAGD). A method to solve the shape-preserving variational spline approximation problem for hole filling in generalized offset surfaces is presented. The existence and uniqueness of the solution of the studied method are established, as well as the computation, and certain convergence results are analyzed. A graphic and numerical example complete this study to demonstrate the effectiveness of the presented method. This manuscript presents the resolution of a complicated problem due to the study of some criteria that can be traduced via an approximation problem related to generalized offset surfaces with holes and also the preservation of the shape of such surfaces.

show abstract

Section: Introductionmentioning

confidence: 99%

A Shape-Preserving Variational Spline Approximation Problem for Hole Filling in Generalized Offset Surfaces

Kouibia,

Pasadas,

Omri

2024

Mathematics

View full text Add to dashboard Cite

show abstract

Collocation Finite Element Method for the Fractional Fokker–Planck Equation

Karabenli,

Esen,

Uçar

2024

Numerical Methods in Fluids

View full text Add to dashboard Cite

In this study, the approximate results of the fractional Fokker–Planck equations have been investigated. First, finite element schemes have been obtained using collocation finite element method based on the trigonometric quintic B‐spline basis functions. Then, the present method is tested on two fundamental problems having appropriate initial conditions. The newly obtained numerical results contained the error norms and for various temporal and spatial steps are compared with the exact ones and other solutions. More accurate results have been obtained for large numbers of spatial and temporal elements.

show abstract

Double Tchebyshev Spectral Tau Algorithm for Solving KdV Equation, with Soliton Application

Youssri

Atta

2022

Encyclopedia of Complexity and Systems Science Series

View full text Add to dashboard Cite

Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments

Cited by 12 publications

References 60 publications

A Shape-Preserving Variational Spline Approximation Problem for Hole Filling in Generalized Offset Surfaces

A Shape-Preserving Variational Spline Approximation Problem for Hole Filling in Generalized Offset Surfaces

Collocation Finite Element Method for the Fractional Fokker–Planck Equation

Double Tchebyshev Spectral Tau Algorithm for Solving KdV Equation, with Soliton Application

Contact Info

Product

Resources

About