Implicit numerical technique for solving fractional Navier-Stoks equation with non-singular kernel
Abstract The nonlinear Burgers equation as a partial differential equation occurs in most physical and mathematical fields such as traffic flow. The equation is extracted from the Navier–Stokes equation by omission of the pressure terms. The effects of two topics are combined with Burgers equation a...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-08-01
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| Series: | Advanced Modeling and Simulation in Engineering Sciences |
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| Online Access: | https://doi.org/10.1186/s40323-025-00300-x |
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| author | L. Azami A. H. Refahi Sheikhani H. Saberi Najafi |
| author_facet | L. Azami A. H. Refahi Sheikhani H. Saberi Najafi |
| author_sort | L. Azami |
| collection | DOAJ |
| description | Abstract The nonlinear Burgers equation as a partial differential equation occurs in most physical and mathematical fields such as traffic flow. The equation is extracted from the Navier–Stokes equation by omission of the pressure terms. The effects of two topics are combined with Burgers equation as the diffusive and nonlinear effects. In the present study, using Crank–Nicholson finite difference technique such a problem is handled and the fractional derivative is approximated using the fractional Caputo-Fabrizio derivative. Convergence and stability are examined. Thus, the suggested scheme is stable unconditionally and includes first and second-order accuracy in time and space. A comparison was made between the numerical results with those of exact solutions. |
| format | Article |
| id | doaj-art-599178de59cd401b81a204c6d387dc37 |
| institution | DOAJ |
| issn | 2213-7467 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advanced Modeling and Simulation in Engineering Sciences |
| spelling | doaj-art-599178de59cd401b81a204c6d387dc372025-08-20T03:05:11ZengSpringerOpenAdvanced Modeling and Simulation in Engineering Sciences2213-74672025-08-0112111810.1186/s40323-025-00300-xImplicit numerical technique for solving fractional Navier-Stoks equation with non-singular kernelL. Azami0A. H. Refahi Sheikhani1H. Saberi Najafi2Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad UniversityDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad UniversityDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad UniversityAbstract The nonlinear Burgers equation as a partial differential equation occurs in most physical and mathematical fields such as traffic flow. The equation is extracted from the Navier–Stokes equation by omission of the pressure terms. The effects of two topics are combined with Burgers equation as the diffusive and nonlinear effects. In the present study, using Crank–Nicholson finite difference technique such a problem is handled and the fractional derivative is approximated using the fractional Caputo-Fabrizio derivative. Convergence and stability are examined. Thus, the suggested scheme is stable unconditionally and includes first and second-order accuracy in time and space. A comparison was made between the numerical results with those of exact solutions.https://doi.org/10.1186/s40323-025-00300-xNavier–Stokes equationFractional Burgers equationTraffic flowNon-singular kernelCaputo-Fabrizio derivativeFinite difference scheme |
| spellingShingle | L. Azami A. H. Refahi Sheikhani H. Saberi Najafi Implicit numerical technique for solving fractional Navier-Stoks equation with non-singular kernel Advanced Modeling and Simulation in Engineering Sciences Navier–Stokes equation Fractional Burgers equation Traffic flow Non-singular kernel Caputo-Fabrizio derivative Finite difference scheme |
| title | Implicit numerical technique for solving fractional Navier-Stoks equation with non-singular kernel |
| title_full | Implicit numerical technique for solving fractional Navier-Stoks equation with non-singular kernel |
| title_fullStr | Implicit numerical technique for solving fractional Navier-Stoks equation with non-singular kernel |
| title_full_unstemmed | Implicit numerical technique for solving fractional Navier-Stoks equation with non-singular kernel |
| title_short | Implicit numerical technique for solving fractional Navier-Stoks equation with non-singular kernel |
| title_sort | implicit numerical technique for solving fractional navier stoks equation with non singular kernel |
| topic | Navier–Stokes equation Fractional Burgers equation Traffic flow Non-singular kernel Caputo-Fabrizio derivative Finite difference scheme |
| url | https://doi.org/10.1186/s40323-025-00300-x |
| work_keys_str_mv | AT lazami implicitnumericaltechniqueforsolvingfractionalnavierstoksequationwithnonsingularkernel AT ahrefahisheikhani implicitnumericaltechniqueforsolvingfractionalnavierstoksequationwithnonsingularkernel AT hsaberinajafi implicitnumericaltechniqueforsolvingfractionalnavierstoksequationwithnonsingularkernel |