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On a Numerical Liapunov--Schmidt Spectral Method and Its Application to Biological Pattern Formation
Spectral expansions are used to provide a basis which preserves continuous symmetries. We show that spectral methods satisfy the conditions for convergence of numerical Liapunov--Schmidt methods. An explicit algorithm for the calculation of stationary bifurcation scenarios near primary instabilities...
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| Published in: | SIAM journal on numerical analysis 2002-01, Vol.40 (2), p.683-701 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c272t-d7be874344ee50709605a98f8920b895962de48291b570fac245e3d38fb3aa9e3 |
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| cites | cdi_FETCH-LOGICAL-c272t-d7be874344ee50709605a98f8920b895962de48291b570fac245e3d38fb3aa9e3 |
| container_end_page | 701 |
| container_issue | 2 |
| container_start_page | 683 |
| container_title | SIAM journal on numerical analysis |
| container_volume | 40 |
| creator | Böhmer, K. Geiger, C. Rodriguez, J. D. |
| description | Spectral expansions are used to provide a basis which preserves continuous symmetries. We show that spectral methods satisfy the conditions for convergence of numerical Liapunov--Schmidt methods. An explicit algorithm for the calculation of stationary bifurcation scenarios near primary instabilities in general continuous symmetric equations is given. The above convergence is extended to $ \Gamma$-equivalent discrete and original bifurcation scenarios. The method is applied to a biologically motivated reaction-diffusion system with spherical symmetry forming patterns. A specific singularity of a generic steady state bifurcation is investigated in detail. |
| doi_str_mv | 10.1137/S0036142998339526 |
| format | article |
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| fulltext | fulltext |
| identifier | ISSN: 0036-1429 |
| ispartof | SIAM journal on numerical analysis, 2002-01, Vol.40 (2), p.683-701 |
| issn | 0036-1429 1095-7170 |
| language | eng |
| recordid | cdi_proquest_journals_922330957 |
| source | SIAM Journals Archive; ABI/INFORM global; JSTOR Archival Journals |
| subjects | Algorithms Methods Navier-Stokes equations Symmetry |
| title | On a Numerical Liapunov--Schmidt Spectral Method and Its Application to Biological Pattern Formation |
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