Numerical solutions of the initial boundary value problem for the perturbed conformable time Korteweg‐de Vries equation by using the finite element method

In this paper, we investigate the initial‐boundary‐value problem for the nonhomogeneous Korteweg‐de Vries equation with conformable derivative on time part of it. We use the finite element method with B‐spline as the basis functions for obtaining the numerical solutions for this nonlinear equation....

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Published in:Numerical methods for partial differential equations Vol. 37; no. 2; pp. 1449 - 1463
Main Authors: Pedram, Leila, Rostamy, Davoud
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.03.2021
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ISSN:0749-159X, 1098-2426
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Abstract In this paper, we investigate the initial‐boundary‐value problem for the nonhomogeneous Korteweg‐de Vries equation with conformable derivative on time part of it. We use the finite element method with B‐spline as the basis functions for obtaining the numerical solutions for this nonlinear equation. In addition, we prove a posteriori and a priori errors for it. These show the adaptivity and convergence of our method. Also, a posteriori error estimate concludes that the error estimate decreases as α increases. We show the accuracy of our work by comparing with the exact solution for the homogeneous KdV equation. We also bring an example for the nonhomogeneous conformable time KdV equation to demonstrate the accuracy and efficiency of the proposed method. Also, these numerical results are consistent with the result of theorems. The numerical results are given in tables and figures.
AbstractList In this paper, we investigate the initial‐boundary‐value problem for the nonhomogeneous Korteweg‐de Vries equation with conformable derivative on time part of it. We use the finite element method with B‐spline as the basis functions for obtaining the numerical solutions for this nonlinear equation. In addition, we prove a posteriori and a priori errors for it. These show the adaptivity and convergence of our method. Also, a posteriori error estimate concludes that the error estimate decreases as α increases. We show the accuracy of our work by comparing with the exact solution for the homogeneous KdV equation. We also bring an example for the nonhomogeneous conformable time KdV equation to demonstrate the accuracy and efficiency of the proposed method. Also, these numerical results are consistent with the result of theorems. The numerical results are given in tables and figures.
In this paper, we investigate the initial‐boundary‐value problem for the nonhomogeneous Korteweg‐de Vries equation with conformable derivative on time part of it. We use the finite element method with B‐spline as the basis functions for obtaining the numerical solutions for this nonlinear equation. In addition, we prove a posteriori and a priori errors for it. These show the adaptivity and convergence of our method. Also, a posteriori error estimate concludes that the error estimate decreases as α increases. We show the accuracy of our work by comparing with the exact solution for the homogeneous KdV equation. We also bring an example for the nonhomogeneous conformable time KdV equation to demonstrate the accuracy and efficiency of the proposed method. Also, these numerical results are consistent with the result of theorems. The numerical results are given in tables and figures.
Author Rostamy, Davoud
Pedram, Leila
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  surname: Rostamy
  fullname: Rostamy, Davoud
  email: rostamy@khayam.ut.ac.ir
  organization: Imam Khomeini International University
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Snippet In this paper, we investigate the initial‐boundary‐value problem for the nonhomogeneous Korteweg‐de Vries equation with conformable derivative on time part of...
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SubjectTerms Basis functions
Boundary value problems
B‐spline
conformable derivative
error estimate
Exact solutions
Finite element analysis
Finite element method
Korteweg-Devries equation
Korteweg‐de Vries equation
nonhomogeneous partial differential equation
Nonlinear equations
Title Numerical solutions of the initial boundary value problem for the perturbed conformable time Korteweg‐de Vries equation by using the finite element method
URI https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fnum.22590
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Volume 37
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