An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation
Abstract In this paper, our purpose is to present a wavelet Galerkin method for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation, which describes nonlinear physical phenomena and involves instability, dissipation, and dispersion parameters. The presented computational method in this p...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-09-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2297-8 |
| _version_ | 1811193471081381888 |
|---|---|
| author | Aydin Secer Neslihan Ozdemir |
| author_facet | Aydin Secer Neslihan Ozdemir |
| author_sort | Aydin Secer |
| collection | DOAJ |
| description | Abstract In this paper, our purpose is to present a wavelet Galerkin method for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation, which describes nonlinear physical phenomena and involves instability, dissipation, and dispersion parameters. The presented computational method in this paper is based on Gegenbauer wavelets. Gegenbauer wavelets have useful properties. Gegenbauer wavelets and the operational matrix of integration, together with the Galerkin method, were used to transform the time-fractional KBK equation into the corresponding nonlinear system of algebraic equations, which can be solved numerically with Newton’s method. Our aim is to show that the Gegenbauer wavelets-based method is efficient and powerful tool for solving the KBK equation with time-fractional derivative. In order to compare the obtained numerical results of the wavelet Galerkin method with exact solutions, two test problems were chosen. The obtained results prove the performance and efficiency of the presented method. |
| first_indexed | 2024-04-12T00:09:02Z |
| format | Article |
| id | doaj.art-15abef00401345d8b029d80731ab7d30 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-12T00:09:02Z |
| publishDate | 2019-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-15abef00401345d8b029d80731ab7d302022-12-22T03:56:01ZengSpringerOpenAdvances in Difference Equations1687-18472019-09-012019111910.1186/s13662-019-2297-8An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equationAydin Secer0Neslihan Ozdemir1Department of Mathematical Engineering, Yildiz Technical UniversityDepartment of Mathematical Engineering, Yildiz Technical UniversityAbstract In this paper, our purpose is to present a wavelet Galerkin method for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation, which describes nonlinear physical phenomena and involves instability, dissipation, and dispersion parameters. The presented computational method in this paper is based on Gegenbauer wavelets. Gegenbauer wavelets have useful properties. Gegenbauer wavelets and the operational matrix of integration, together with the Galerkin method, were used to transform the time-fractional KBK equation into the corresponding nonlinear system of algebraic equations, which can be solved numerically with Newton’s method. Our aim is to show that the Gegenbauer wavelets-based method is efficient and powerful tool for solving the KBK equation with time-fractional derivative. In order to compare the obtained numerical results of the wavelet Galerkin method with exact solutions, two test problems were chosen. The obtained results prove the performance and efficiency of the presented method.http://link.springer.com/article/10.1186/s13662-019-2297-8Galerkin methodGegenbauer waveletsKdV-Burgers-Kuramoto (KBK) equationOperational matrix of integration |
| spellingShingle | Aydin Secer Neslihan Ozdemir An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation Advances in Difference Equations Galerkin method Gegenbauer wavelets KdV-Burgers-Kuramoto (KBK) equation Operational matrix of integration |
| title | An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation |
| title_full | An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation |
| title_fullStr | An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation |
| title_full_unstemmed | An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation |
| title_short | An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation |
| title_sort | effective computational approach based on gegenbauer wavelets for solving the time fractional kdv burgers kuramoto equation |
| topic | Galerkin method Gegenbauer wavelets KdV-Burgers-Kuramoto (KBK) equation Operational matrix of integration |
| url | http://link.springer.com/article/10.1186/s13662-019-2297-8 |
| work_keys_str_mv | AT aydinsecer aneffectivecomputationalapproachbasedongegenbauerwaveletsforsolvingthetimefractionalkdvburgerskuramotoequation AT neslihanozdemir aneffectivecomputationalapproachbasedongegenbauerwaveletsforsolvingthetimefractionalkdvburgerskuramotoequation AT aydinsecer effectivecomputationalapproachbasedongegenbauerwaveletsforsolvingthetimefractionalkdvburgerskuramotoequation AT neslihanozdemir effectivecomputationalapproachbasedongegenbauerwaveletsforsolvingthetimefractionalkdvburgerskuramotoequation |