New numerical solutions of fractional-order Korteweg-de Vries equation
We present new solutions of fractional-order Korteweg-de Vries (KdV) equation by employing a method that utilizes advantages of both techniques of fictititous time integration and group preserving. Proposed method converts the KdV to a new system of equations which is approximately solved by a semi-...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2020-12-01
|
| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379720317939 |
| _version_ | 1818383853052493824 |
|---|---|
| author | Mustafa Inc Mohammad Parto-Haghighi Mehmet Ali Akinlar Yu-Ming Chu |
| author_facet | Mustafa Inc Mohammad Parto-Haghighi Mehmet Ali Akinlar Yu-Ming Chu |
| author_sort | Mustafa Inc |
| collection | DOAJ |
| description | We present new solutions of fractional-order Korteweg-de Vries (KdV) equation by employing a method that utilizes advantages of both techniques of fictititous time integration and group preserving. Proposed method converts the KdV to a new system of equations which is approximately solved by a semi-discretization numerical scheme. Caputo type fractional-order derivative operators are used. We apply the method to some specific cases of the KdV equation. Computational results indicate that the method gives new and highly efficient solutions of the KdV equation. |
| first_indexed | 2024-12-14T03:12:58Z |
| format | Article |
| id | doaj.art-7afdec4e17d14722838681926ab6ed27 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-14T03:12:58Z |
| publishDate | 2020-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-7afdec4e17d14722838681926ab6ed272022-12-21T23:19:12ZengElsevierResults in Physics2211-37972020-12-0119103326New numerical solutions of fractional-order Korteweg-de Vries equationMustafa Inc0Mohammad Parto-Haghighi1Mehmet Ali Akinlar2Yu-Ming Chu3Department of Mathematics, Firat University, Elazig, Turkey; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, TaiwanDepartment of Mathematics, University of Bonab, Bonab, IranDepartment of Mathematical Engineering, Yildiz Technical University, Istanbul, TurkeyDepartment of Mathematics, Huzhou University, Huzhou 313000, China; Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, China; Corresponding author at: Department of Mathematics, Huzhou University, Huzhou 313000, China.We present new solutions of fractional-order Korteweg-de Vries (KdV) equation by employing a method that utilizes advantages of both techniques of fictititous time integration and group preserving. Proposed method converts the KdV to a new system of equations which is approximately solved by a semi-discretization numerical scheme. Caputo type fractional-order derivative operators are used. We apply the method to some specific cases of the KdV equation. Computational results indicate that the method gives new and highly efficient solutions of the KdV equation.http://www.sciencedirect.com/science/article/pii/S2211379720317939Time fractional Korteweg de Vries equationFictitious time integrationGroup preserving scheme (GPS)Caputo derivative |
| spellingShingle | Mustafa Inc Mohammad Parto-Haghighi Mehmet Ali Akinlar Yu-Ming Chu New numerical solutions of fractional-order Korteweg-de Vries equation Results in Physics Time fractional Korteweg de Vries equation Fictitious time integration Group preserving scheme (GPS) Caputo derivative |
| title | New numerical solutions of fractional-order Korteweg-de Vries equation |
| title_full | New numerical solutions of fractional-order Korteweg-de Vries equation |
| title_fullStr | New numerical solutions of fractional-order Korteweg-de Vries equation |
| title_full_unstemmed | New numerical solutions of fractional-order Korteweg-de Vries equation |
| title_short | New numerical solutions of fractional-order Korteweg-de Vries equation |
| title_sort | new numerical solutions of fractional order korteweg de vries equation |
| topic | Time fractional Korteweg de Vries equation Fictitious time integration Group preserving scheme (GPS) Caputo derivative |
| url | http://www.sciencedirect.com/science/article/pii/S2211379720317939 |
| work_keys_str_mv | AT mustafainc newnumericalsolutionsoffractionalorderkortewegdevriesequation AT mohammadpartohaghighi newnumericalsolutionsoffractionalorderkortewegdevriesequation AT mehmetaliakinlar newnumericalsolutionsoffractionalorderkortewegdevriesequation AT yumingchu newnumericalsolutionsoffractionalorderkortewegdevriesequation |