A Quartic Subdomain Finite Element Method for the Modified KdV Equation

Karakoç, Seydi Battal Gazi

doi:10.19139/soic.v6i4.485

Cited by 7 publications

(2 citation statements)

References 24 publications

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“…In this section, the two well-known test problems are investigated namely motion of shock wave and evolution of solitary waves with Gaussian initial condition. The accuracy of the present numerical method is controlled using the following error norms, L 2 and L ∞ , respectively [33]:…”

Section: Computer Applications and Discussionmentioning

confidence: 99%

Numerical Simulation of Generalized Oskolkov Equation via the Septic B-Spline Collocation Method

Karakoç

Sucu

TAGHACHİ

2022

Journal of Universal Mathematics

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In this paper, one of the nonlinear evolution equation (NLEE) namely generalised Oskolkov equation which defines the dynamics of an incompressible visco-elastic Kelvin-Voigt fluid is investigated. We discuss numerical solutions of the equation for two test problems including single solitary wave and Gaussian initial condition, applying the collocation finite element method. The algorithm, based upon Crank Nicolson approach in time, is unconditionally stable. To demonstrate the proficiency and accuracy of the numerical algorithm, error norms L2, L∞ and invariant I are calculated and the obtained results are indicated both in tabular and graphical form. The obtained numerical results provide the method is more suitable and systematically handle the solution procedures of nonlinear equations arising in mathematical physics.

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Section: Computer Applications and Discussionmentioning

confidence: 99%

Numerical Simulation of Generalized Oskolkov Equation via the Septic B-Spline Collocation Method

Karakoç

Sucu

TAGHACHİ

2022

Journal of Universal Mathematics

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“…Convergence stability is considered when 5 consecutive N bar errors are tempted to be below 3%, similarly to the iterative schemes outlined in [30]. The mathematical formulation of N IP min and N min bar are represented by expressions 10 and 11; the relative errors ϵ N IP and ϵ bar were expressed following the approach adopted by [31] for the estimation of errors between the corresponding exact solution and the approximated solution.…”

Section: Energy Convergence Criteriamentioning

confidence: 99%

Finite Element modeling and convergence analysis of a new Biomimetic Branching Structure.

RIHANI,

Akhrif,

El Jai

et al. 2024

Stat., optim. inf. comput.

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Branching structures are gaining popularity in the field of advanced structures and building design; they offer high performance in terms of strength and lightweight design, along with the flexibility and precision enabled by modern processing technologies like Additive Manufacturing. This paper provides a concise overview of a geometric design procedure for a novel ribbed class of structures which was previously developed by the authors as a biomimetic optimal Micro-architected dome. Hereinafter, linear lattice models are suggested to carry out structural calculations using the finite element method (FEM). The objective is to examine discretization thresholding and strain energy convergence criteria. Results show that convergence is reached for numbers of elements per leg, ranging from 2 to 6, depending on the geometrical configuration of the dome being studied. The strain energy balance also exposes the influence of each internal force on the total mechanical response of the structure, pinpointing bending moment and axial force as the main decisive factors. As a perspective, the study will focus on limit state design calculations and Analysis of how the local geometry influences the overall stability and strength of this new design.

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

Başhan

2021

Applied Numerical Mathematics

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A Quartic Subdomain Finite Element Method for the Modified KdV Equation

Cited by 7 publications

References 24 publications

Numerical Simulation of Generalized Oskolkov Equation via the Septic B-Spline Collocation Method

Numerical Simulation of Generalized Oskolkov Equation via the Septic B-Spline Collocation Method

Finite Element modeling and convergence analysis of a new Biomimetic Branching Structure.

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

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