A time-space B-spline integrator for the Burgers' equation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918158230618112 |
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| author | Dag, Idris Uğurluoğlu, Serkan Adar, Nihat |
| author_facet | Dag, Idris Uğurluoğlu, Serkan Adar, Nihat |
| contents | The purpose of this paper is to propose a new algorithm for obtaining approximate solutions to the Burgers' equation (BE). Integration in time by a quadratic B-spline collocation method is shown. To the best of our knowledge, B-splines have not previously been used to integrate partial differential equations in both time and space. First, the BE is integrated using quadratic B-spline functions in time, and then the time-integrated BE is further solved in space via the cubic B-spline collocation method. The resulting recursive algebraic equation is used to obtain both shock wave and front propagation solutions of the BE, demonstrating the effectiveness of the space--time B-spline collocation method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09408 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A time-space B-spline integrator for the Burgers' equation Dag, Idris Uğurluoğlu, Serkan Adar, Nihat Numerical Analysis The purpose of this paper is to propose a new algorithm for obtaining approximate solutions to the Burgers' equation (BE). Integration in time by a quadratic B-spline collocation method is shown. To the best of our knowledge, B-splines have not previously been used to integrate partial differential equations in both time and space. First, the BE is integrated using quadratic B-spline functions in time, and then the time-integrated BE is further solved in space via the cubic B-spline collocation method. The resulting recursive algebraic equation is used to obtain both shock wave and front propagation solutions of the BE, demonstrating the effectiveness of the space--time B-spline collocation method. |
| title | A time-space B-spline integrator for the Burgers' equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.09408 |