Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation
This paper presents a novel numerical spectral scheme to handle the time-fractional KdV–Burgers’ equation, which is very important in both physics and engineering. The scheme basically uses the tau approach combined with Gegenbauer polynomials to provide accurate and stable numerical solutions. Inst...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
|
| Series: | Mathematical and Computational Applications |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2297-8747/29/6/107 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846103827003998208 |
|---|---|
| author | Youssri Hassan Youssri Ahmed Gamal Atta |
| author_facet | Youssri Hassan Youssri Ahmed Gamal Atta |
| author_sort | Youssri Hassan Youssri |
| collection | DOAJ |
| description | This paper presents a novel numerical spectral scheme to handle the time-fractional KdV–Burgers’ equation, which is very important in both physics and engineering. The scheme basically uses the tau approach combined with Gegenbauer polynomials to provide accurate and stable numerical solutions. Instead of solving the differential problem together with the conditions, we solve a system of algebraic equations. The method can handle complex boundary conditions. Some numerical experiments are exhibited to demonstrate that this approach is highly efficient and produces results that are better than some existing numerical methods in the literature. This technique offers more advanced solutions for time-fractional problems in various fields. |
| format | Article |
| id | doaj-art-eea7485e46c74ba181c84b13bd1b53c9 |
| institution | Kabale University |
| issn | 1300-686X 2297-8747 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj-art-eea7485e46c74ba181c84b13bd1b53c92024-12-27T14:38:26ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472024-11-0129610710.3390/mca29060107Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ EquationYoussri Hassan Youssri0Ahmed Gamal Atta1Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, EgyptThis paper presents a novel numerical spectral scheme to handle the time-fractional KdV–Burgers’ equation, which is very important in both physics and engineering. The scheme basically uses the tau approach combined with Gegenbauer polynomials to provide accurate and stable numerical solutions. Instead of solving the differential problem together with the conditions, we solve a system of algebraic equations. The method can handle complex boundary conditions. Some numerical experiments are exhibited to demonstrate that this approach is highly efficient and produces results that are better than some existing numerical methods in the literature. This technique offers more advanced solutions for time-fractional problems in various fields.https://www.mdpi.com/2297-8747/29/6/107Gegenbauer polynomialsPetrov–Galerkin methodtime-fractional KdV–Burgers’ equation |
| spellingShingle | Youssri Hassan Youssri Ahmed Gamal Atta Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation Mathematical and Computational Applications Gegenbauer polynomials Petrov–Galerkin method time-fractional KdV–Burgers’ equation |
| title | Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation |
| title_full | Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation |
| title_fullStr | Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation |
| title_full_unstemmed | Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation |
| title_short | Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation |
| title_sort | radical petrov galerkin approach for the time fractional kdv burgers equation |
| topic | Gegenbauer polynomials Petrov–Galerkin method time-fractional KdV–Burgers’ equation |
| url | https://www.mdpi.com/2297-8747/29/6/107 |
| work_keys_str_mv | AT youssrihassanyoussri radicalpetrovgalerkinapproachforthetimefractionalkdvburgersequation AT ahmedgamalatta radicalpetrovgalerkinapproachforthetimefractionalkdvburgersequation |