A numerical study of stiffness effects on some high order splitting methods
Fuente:
Universidad Nacional Autónoma de México
Resumen: In this paper we compare operator splitting methods of first, second, third and fourth orders that are applied to problems with stiff matrices. In order to efficiently solve the resultant subproblems is necessary to use implicit Runge-Kutta methods. It is known that, in this context, the pr...
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| Format: | Artículo de Investigación |
| Language: | English |
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Sociedad Mexicana de Física, A.C.
2006
Universidad Nacional Autónoma de México; Facultad de Ciencias |
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| _version_ | 1877697776616210433 |
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| author | Salcedo Ruíz, J. Sánchez Bernabe, F. J. |
| author_facet | Salcedo Ruíz, J. Sánchez Bernabe, F. J. |
| author_sort | Salcedo Ruíz, J. |
| collection | Repositorio Institucional UNAM |
| description | Resumen: In this paper we compare operator splitting methods of first, second, third and fourth orders that are applied to problems with stiff matrices. In order to efficiently solve the resultant subproblems is necessary to use implicit Runge-Kutta methods. It is known that, in this context, the precision order of operator splitting schemes is reduced. Furthermore, we propose a fifth order operator splitting method that is obtained by applying Richardson extrapolation to a fourth order method. All methods are tested with a model problem with matrices such that its condition number is taken up to 20,000. Our conclusion is that order reduction is more severe for low order operator splitting methods. |
| format | Artículo de Investigación |
| id | unam-41311 |
| institution | Universidad Nacional Autónoma de México |
| language | English |
| publishDate | 2006 |
| publisher | Sociedad Mexicana de Física, A.C. Universidad Nacional Autónoma de México; Facultad de Ciencias |
| record_format | dspace |
| spelling | A numerical study of stiffness effects on some high order splitting methods Salcedo Ruíz, J. Sánchez Bernabe, F. J. Físico Matemáticas y Ciencias de la Tierra Operator splitting stiff matrix Richardson extrapolation implicit Runge-Kutta methods Procedencia: Universidad Nacional Autónoma de México Repositorio Institucional de la UNAM: https://repositorio.unam.mx/ Resumen: In this paper we compare operator splitting methods of first, second, third and fourth orders that are applied to problems with stiff matrices. In order to efficiently solve the resultant subproblems is necessary to use implicit Runge-Kutta methods. It is known that, in this context, the precision order of operator splitting schemes is reduced. Furthermore, we propose a fifth order operator splitting method that is obtained by applying Richardson extrapolation to a fourth order method. All methods are tested with a model problem with matrices such that its condition number is taken up to 20,000. Our conclusion is that order reduction is more severe for low order operator splitting methods. Sociedad Mexicana de Física, A.C. Universidad Nacional Autónoma de México; Facultad de Ciencias 2006-01-01 Text Artículo de Investigación application/pdf Cita bibliográfica: Salcedo Ruíz, J., et al. (2006). A numerical study of stiffness effects on some high order splitting methods. Revista Mexicana de Física; Vol 52, No 2: 129-0. Recuperado de https://rmf.smf.mx/ojs/rmf/article/view/3440 ISSN: 2683-2224 (digital); 0035-001X (impresa) https://repositorio.unam.mx/contenidos/41311 eng Revista Mexicana de Física; Vol 52, No 2 (2006): 129-0 https://rmf.smf.mx/ojs/rmf/index Nivel de acceso: Público La titularidad de los derechos patrimoniales de esta obra pertenece a las instituciones editoras. Su uso se rige por una licencia Creative Commons BY-NC-ND 4.0 Internacional, https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode.es, fecha de asignación de la licencia 2006-01-01, para un uso diferente consultar al responsable jurídico del repositorio por medio de rmf@ciencias.unam.mx |
| spellingShingle | A numerical study of stiffness effects on some high order splitting methods Salcedo Ruíz, J. Sánchez Bernabe, F. J. Físico Matemáticas y Ciencias de la Tierra Operator splitting stiff matrix Richardson extrapolation implicit Runge-Kutta methods |
| title | A numerical study of stiffness effects on some high order splitting methods |
| title_full | A numerical study of stiffness effects on some high order splitting methods |
| title_fullStr | A numerical study of stiffness effects on some high order splitting methods |
| title_full_unstemmed | A numerical study of stiffness effects on some high order splitting methods |
| title_short | A numerical study of stiffness effects on some high order splitting methods |
| title_sort | a numerical study of stiffness effects on some high order splitting methods |
| topic | Físico Matemáticas y Ciencias de la Tierra Operator splitting stiff matrix Richardson extrapolation implicit Runge-Kutta methods |
| topic_facet | Físico Matemáticas y Ciencias de la Tierra Operator splitting stiff matrix Richardson extrapolation implicit Runge-Kutta methods |
| url | https://repositorio.unam.mx/contenidos/41311 |