A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems
<p>In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit–explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Ch...
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| Format: | Journal article |
| Language: | English |
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Elsevier
2010
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| _version_ | 1797051807962234880 |
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| author | Muite, B |
| author2 | Care, M |
| author_facet | Care, M Muite, B |
| author_sort | Muite, B |
| collection | OXFORD |
| description | <p>In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit–explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Chebyshev collocation method to do this, the accuracy of the real space Chebyshev differentiation, spectral space preconditioned Chebyshev tau, real space Chebyshev integration and spectral space Chebyshev integration methods are compared in the <em>L<sup>2</sup></em> and <em>W<sup>2,2</sup></em> norms when solving linear fourth order boundary value problems; and in the <em>L<sup>∞</sup></em>([0,<em>T</em>]; <em>L<sup>2</sup></em>) and <em>L<sup>∞</sup></em>([0,<em>T</em>]; <em>W<sup>2,2</sup></em>) norms when solving initial boundary value problems. We find that the best Chebyshev method to use for high resolution computations of solutions to initial boundary value problems is the spectral space Chebyshev integration method which uses sparse matrix operations and has a computational cost comparable to Fourier spectral discretization.</p> |
| first_indexed | 2024-03-06T18:24:36Z |
| format | Journal article |
| id | oxford-uuid:07830f41-ea32-4351-8baa-219c727e1d8d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:24:36Z |
| publishDate | 2010 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:07830f41-ea32-4351-8baa-219c727e1d8d2022-03-26T09:07:52ZA numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:07830f41-ea32-4351-8baa-219c727e1d8dComputer science (mathematics)MathematicsEnglishOxford University Research Archive - ValetElsevier2010Muite, BCare, M<p>In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit–explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Chebyshev collocation method to do this, the accuracy of the real space Chebyshev differentiation, spectral space preconditioned Chebyshev tau, real space Chebyshev integration and spectral space Chebyshev integration methods are compared in the <em>L<sup>2</sup></em> and <em>W<sup>2,2</sup></em> norms when solving linear fourth order boundary value problems; and in the <em>L<sup>∞</sup></em>([0,<em>T</em>]; <em>L<sup>2</sup></em>) and <em>L<sup>∞</sup></em>([0,<em>T</em>]; <em>W<sup>2,2</sup></em>) norms when solving initial boundary value problems. We find that the best Chebyshev method to use for high resolution computations of solutions to initial boundary value problems is the spectral space Chebyshev integration method which uses sparse matrix operations and has a computational cost comparable to Fourier spectral discretization.</p> |
| spellingShingle | Computer science (mathematics) Mathematics Muite, B A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems |
| title | A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems |
| title_full | A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems |
| title_fullStr | A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems |
| title_full_unstemmed | A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems |
| title_short | A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems |
| title_sort | numerical comparison of chebyshev methods for solving fourth order semilinear initial boundary value problems |
| topic | Computer science (mathematics) Mathematics |
| work_keys_str_mv | AT muiteb anumericalcomparisonofchebyshevmethodsforsolvingfourthordersemilinearinitialboundaryvalueproblems AT muiteb numericalcomparisonofchebyshevmethodsforsolvingfourthordersemilinearinitialboundaryvalueproblems |