Using the spectral meshless radial basis functions method for solving time fractional Burgers’ equation
Abstract This study presents a local meshless method based on radial basis functions for the numerical solution of the nonlinear time-fractional Burgers’ equation (TFBE) involving the fractional derivatives of Caputo (CFD) and Caputo–Fabrizio (CFFD). Time is discretized using the implicit finite dif...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-07-01
|
| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-025-02075-x |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849234683849605120 |
|---|---|
| author | S. Hajiollow F. Zabihi |
| author_facet | S. Hajiollow F. Zabihi |
| author_sort | S. Hajiollow |
| collection | DOAJ |
| description | Abstract This study presents a local meshless method based on radial basis functions for the numerical solution of the nonlinear time-fractional Burgers’ equation (TFBE) involving the fractional derivatives of Caputo (CFD) and Caputo–Fabrizio (CFFD). Time is discretized using the implicit finite difference scheme with θ = 1 $\theta = 1$ , while radial basis functions (RBFs), which do not require a mesh to approximate the solution, are used for spatial discretization. The Rubin–Graves technique is used to linearize nonlinear terms. Approximation of the existing spatial derivatives is done using central and finite difference methods, and the temporal derivatives are approximated by using the definition of Caputo and Caputo–Fabrizio derivatives. With the mentioned techniques, a system of algebraic equations is established. By comparing the results obtained from solving this system with the previous results, it is clear that the presented technique provides accurate, stable, and convergent results. |
| format | Article |
| id | doaj-art-5402b02adc3d4bb594239a6cbde53111 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-5402b02adc3d4bb594239a6cbde531112025-08-20T04:03:03ZengSpringerOpenBoundary Value Problems1687-27702025-07-012025112110.1186/s13661-025-02075-xUsing the spectral meshless radial basis functions method for solving time fractional Burgers’ equationS. Hajiollow0F. Zabihi1Department of Applied Mathematics, Faculty of Mathematical Science, University of KashanDepartment of Applied Mathematics, Faculty of Mathematical Science, University of KashanAbstract This study presents a local meshless method based on radial basis functions for the numerical solution of the nonlinear time-fractional Burgers’ equation (TFBE) involving the fractional derivatives of Caputo (CFD) and Caputo–Fabrizio (CFFD). Time is discretized using the implicit finite difference scheme with θ = 1 $\theta = 1$ , while radial basis functions (RBFs), which do not require a mesh to approximate the solution, are used for spatial discretization. The Rubin–Graves technique is used to linearize nonlinear terms. Approximation of the existing spatial derivatives is done using central and finite difference methods, and the temporal derivatives are approximated by using the definition of Caputo and Caputo–Fabrizio derivatives. With the mentioned techniques, a system of algebraic equations is established. By comparing the results obtained from solving this system with the previous results, it is clear that the presented technique provides accurate, stable, and convergent results.https://doi.org/10.1186/s13661-025-02075-xFractional partial differential equationsBurgers’ equationCaputoCaputo–FabrizioMeshless methodRadial basis functions |
| spellingShingle | S. Hajiollow F. Zabihi Using the spectral meshless radial basis functions method for solving time fractional Burgers’ equation Boundary Value Problems Fractional partial differential equations Burgers’ equation Caputo Caputo–Fabrizio Meshless method Radial basis functions |
| title | Using the spectral meshless radial basis functions method for solving time fractional Burgers’ equation |
| title_full | Using the spectral meshless radial basis functions method for solving time fractional Burgers’ equation |
| title_fullStr | Using the spectral meshless radial basis functions method for solving time fractional Burgers’ equation |
| title_full_unstemmed | Using the spectral meshless radial basis functions method for solving time fractional Burgers’ equation |
| title_short | Using the spectral meshless radial basis functions method for solving time fractional Burgers’ equation |
| title_sort | using the spectral meshless radial basis functions method for solving time fractional burgers equation |
| topic | Fractional partial differential equations Burgers’ equation Caputo Caputo–Fabrizio Meshless method Radial basis functions |
| url | https://doi.org/10.1186/s13661-025-02075-x |
| work_keys_str_mv | AT shajiollow usingthespectralmeshlessradialbasisfunctionsmethodforsolvingtimefractionalburgersequation AT fzabihi usingthespectralmeshlessradialbasisfunctionsmethodforsolvingtimefractionalburgersequation |