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semi-discrete-scheme-for-kirchhoff-eqn

This is the numerical implementation section of our preprint, which has been submitted to arXiv under the identifier arXiv:2303.10350.

https://github.com/zv1991/semi-discrete-scheme-for-kirchhoff-eqn

Science Score: 67.0%

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Keywords

cauchy-problem fourth-order-accuracy-three-term-difference-scheme gnu-octave matlab nonlinear-kirchhoff-string-equation three-layer-semi-discrete-scheme
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This is the numerical implementation section of our preprint, which has been submitted to arXiv under the identifier arXiv:2303.10350.

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cauchy-problem fourth-order-accuracy-three-term-difference-scheme gnu-octave matlab nonlinear-kirchhoff-string-equation three-layer-semi-discrete-scheme
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README.md

On Convergence of a Three-layer Semi-discrete Scheme for the Nonlinear Dynamic String Equation of Kirchhoff-type with Time-dependent Coefficients

This paper considers the Cauchy problem for the nonlinear dynamic string equation of Kirchhoff-type with time-varying coefficients. The objective of this work is to develop a temporal discretization algorithm capable of approximating a solution to this initial-boundary value problem. To this end, a symmetric three-layer semi-discrete scheme is employed with respect to the temporal variable, wherein the value of a nonlinear term is evaluated at the middle node point. This approach enables the numerical solutions per temporal step to be obtained by inverting the linear operators, yielding a system of second-order linear ordinary differential equations. Local convergence of the proposed scheme is established, and it achieves quadratic convergence concerning the step size of the discretization of time on the local temporal interval. We have conducted several numerical experiments using the proposed algorithm for various test problems to validate its performance. It can be said that the obtained numerical results are in accordance with the theoretical findings.

 

For more information, see our arXiv preprint: https://arxiv.org/abs/2303.10350.

 

A Programming Code for a Three-Layer Semi-Discrete Scheme for the Nonlinear Dynamic String Equation of Kirchhoff-Type with Time-Dependent Coefficients by Jemal Rogava, Zurab Vashakidze is licensed under CC BY 4.0

 

Cite the code: DOI

Owner

  • Name: Zurab Vashakidze
  • Login: zv1991
  • Kind: user
  • Location: Tbilisi, Georgia

Citation (CITATION.cff) 

cff-version: 1.2.0
message: "If you use this software, please cite it as below."
authors:
- family-names: "Rogava"
  given-names: "Jemal"
  orcid: "https://orcid.org/0000-0001-9460-4283"
- family-names: "Vashakidze"
  given-names: "Zurab"
  orcid: "https://orcid.org/0000-0001-8736-6213"
title: "A Programming Code for a Three-Layer Semi-Discrete Scheme for the Nonlinear Dynamic String Equation of Kirchhoff-Type with Time-Dependent Coefficients"
version: 1.1.0
doi: 10.5281/zenodo.10137813
date-released: 2023-11-15
url: "https://github.com/zv1991/Semi-Discrete-Scheme-for-Kirchhoff-Eqn"

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