A fast algorithm to solve systems of nonlinear equations
A new HSS-based algorithm for solving systems of nonlinear equations is presented and its semilocal convergence is proved. Spectral properties of the new method are investigated. Performance profile for the new scheme is computed and compared with HSS algorithm. Besides, by a numerical example in wh...
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| Published in | Journal of computational and applied mathematics Vol. 354; pp. 242 - 258 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.07.2019
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-0427 1879-1778 1879-1778 |
| DOI | 10.1016/j.cam.2018.03.048 |
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| Abstract | A new HSS-based algorithm for solving systems of nonlinear equations is presented and its semilocal convergence is proved. Spectral properties of the new method are investigated. Performance profile for the new scheme is computed and compared with HSS algorithm. Besides, by a numerical example in which a two-dimensional nonlinear convection–diffusion equation is solved, we compare the new method and the Newton–HSS method. Numerical results show that the new scheme solves the problem faster than the Newton–HSS scheme in terms of CPU-time and number of iterations. Moreover, the application of the new method is found to be fast, reliable, flexible, accurate, and has small CPU time. |
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| AbstractList | A new HSS-based algorithm for solving systems of nonlinear equations is presented and its semilocal convergence is proved. Spectral properties of the new method are investigated. Performance profile for the new scheme is computed and compared with HSS algorithm. Besides, by a numerical example in which a two-dimensional nonlinear convection–diffusion equation is solved, we compare the new method and the Newton–HSS method. Numerical results show that the new scheme solves the problem faster than the Newton–HSS scheme in terms of CPU-time and number of iterations. Moreover, the application of the new method is found to be fast, reliable, flexible, accurate, and has small CPU time. |
| Author | Amiri, Abdolreza Cordero, Alicia Torregrosa, Juan R. Darvishi, Mohammad Taghi |
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| Cites_doi | 10.1002/nla.517 10.1002/nla.713 10.1007/s101070100263 10.1016/S0377-0427(97)00036-8 10.1023/A:1019125332723 10.1137/S0895479801395458 10.1007/s00211-004-0574-1 10.1137/040616048 10.4208/jcm.2009.10-m2836 10.1016/j.jcp.2003.08.010 10.1007/s00211-004-0521-1 10.1016/j.apnum.2009.06.005 10.1016/j.laa.2007.02.018 10.1016/j.apnum.2006.02.007 10.1016/j.camwa.2006.12.024 10.1002/nla.528 |
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| Keywords | Newton–HSS method Iterative method Jacobian free scheme Newton-GPSS method Nonlinear systems Newton method |
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| SubjectTerms | Iterative method Jacobian free scheme Newton method Newton-GPSS method Newton–HSS method Nonlinear systems |
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