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 |
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| Language: | English |
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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. |
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| 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 |
| Author_xml | – sequence: 1 givenname: Leila surname: Pedram fullname: Pedram, Leila organization: Imam Khomeini International University – sequence: 2 givenname: Davoud orcidid: 0000-0001-9585-8904 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 |
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