Avoiding the order reduction when solving second-order in time PDEs with Fractional Step Runge-Kutta-Nyström methods
| dc.contributor.author | Moreta Santos, María Jesús | |
| dc.contributor.author | Bujanda, Blanca | |
| dc.contributor.author | Jorge, Juan Carlos | |
| dc.date.accessioned | 2023-06-18T05:48:59Z | |
| dc.date.available | 2023-06-18T05:48:59Z | |
| dc.date.issued | 2016-04 | |
| dc.description | Preprint del artículo publicado en CAMWA: Article title: Avoiding the order reduction when solving second-order in time PDEs with Fractional Step Runge-Kutta-Nyström methods Article reference: CAMWA8205 Journal title: Computers and Mathematics with Applications Corresponding author: Dr. M. J. Moreta First author: Dr. M. J. Moreta Final version published online: 24-MAR-2016 Full bibliographic details: Computers and Mathematics with Applications 71 (2016), pp. 1425-1447 DOI information: 10.1016/j.camwa.2016.02.015 | |
| dc.description.abstract | We study some of the main features of Fractional Step Runge-Kutta-Nystr¨om methods when they are used to integrate Initial-Boundary Value Problems of second order in time, in combination with a suitable spatial discretization. We focus our attention in the order reduction phenomenon, which appears if classical boundary conditions are taken at the internal stages. This drawback is specially hard when time dependent boundary conditions are considered. In this paper we present an efficient technique, very simple and computationally cheap, which allows us to avoid the order reduction; such technique consists of modifying the boundary conditions for the internal stages of the method. | |
| dc.description.department | Depto. de Análisis Económico y Economía Cuantitativa | |
| dc.description.faculty | Fac. de Ciencias Económicas y Empresariales | |
| dc.description.refereed | FALSE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/43936 | |
| dc.identifier.doi | 10.1016/j.camwa.2016.02.015 | |
| dc.identifier.issn | 0898-1221 | |
| dc.identifier.officialurl | https://doi.org/10.1016/j.camwa.2016.02.015 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/23401 | |
| dc.journal.title | Computers and mathematics with applications | |
| dc.language.iso | eng | |
| dc.page.final | 1447 | |
| dc.page.initial | 1425 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | MTM 2015-66837-P | |
| dc.rights.accessRights | open access | |
| dc.subject.keyword | Fractional Step Runge-Kutta-Nystr¨om methods | |
| dc.subject.keyword | Second-order partial differential equations | |
| dc.subject.keyword | Order reduction | |
| dc.subject.keyword | Stability | |
| dc.subject.keyword | Consistency. | |
| dc.subject.ucm | Matemáticas (Matemáticas) | |
| dc.subject.unesco | 12 Matemáticas | |
| dc.title | Avoiding the order reduction when solving second-order in time PDEs with Fractional Step Runge-Kutta-Nyström methods | |
| dc.type | journal article | |
| dc.volume.number | 71 | |
| dcterms.references | H. Kreiss, B. Gustafsson, and J. Oliger, Time Dependent Problems and Difference Methods. Wiley-Interscience, New York, 1995. “Numerical resolution of linear evolution multidimensional problems of second order in time,” Numer. Methods Partial Differential Equations, vol. 28, no. 2, pp. 597–620, 2012. J. E. D. Jr. and G. Fairweather, “Alternating-direction galerkin methods for parabolic and hyperbolic problems on rectangular polygons,” SIAM J. Numer. Anal., vol. 12, pp. 144–163, 1975. D. W. Peaceman and H. H. Rachford, “The numerical solution of parabolic and elliptic differential equations,” J. SIAM., vol. 3, pp. 28–42, 1955. N. N. Yanenko, The method of fractional steps. The solution of problems of mathematical physics in several variables. Springer-Verlag, New York-Heidelberg, 1971. E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. P. V. D. Houwen, B. Sommeijer, and N. H. Cong, “Stability of collocation-based Runge-kutta-nystr¨om methods,” BIT, vol. 31, pp. 469–481, 1991. G. Fairweather and A. R. Mitchell, “A high accuracy alternating direction method for the wave equation,” J. Inst. Math. Appl., vol. 1, pp. 309–316, 1965. I. Alonso-Mallo, “Runge-kutta methods without order reduction for linear initial boundary value problems,” Numer. Math., vol. 91, pp. 577–603, 2002. M. P. Calvo and C. Palencia, “Avoiding the order reduction of runge-kutta methods for linear initial boundary value problems,” Math. Comp., vol. 71, pp. 1529–1543, 2002. C. Lubich and A. Ostermann, “Interior estimates for time discretizations of parabolic equations,” Appl. Numer. Math., vol. 18, pp. 241–251, 1995. J. G. Verwer, “Convergence and order reduction of diagonally implicit runge-kutta schemes in the method of lines,” in Numerical analysis (Dundee, 1985), vol. 140 of Pitman Res. Notes Math. Ser., pp. 220–237, Longman Sci. Tech., Harlow, 1986. I. Alonso-Mallo, B. Cano, and M. Moreta, “Optimal time order when implicit rungekutta-nystr¨om methods solve linear partial differential equations,” Appl. Numer. Math., vol. 58, no. 5, pp. 539–562, 2008. M. J. Moreta, Discretization of second-order in time partial differential equations by means of Runge-Kutta-Nystr¨om methods. PhD thesis, Department of Applied Mathematics, University of Valladolid, Spain, 2005. J. A. Goldstein, Semigroups of Linear Operators and Applications. Oxford University Press, New York, 1985. C. Bernardi and Y. Maday, Progress in Approximation Theory, ch. Some spectral approximations of one-dimensional fourth-order problems, pp. 43–116. Academic Press, 1991. C. Bernardi and Y. Maday, Approximations spectrales de probl`emes aux limites elliptiques. Springer–Verlag, Paris, 1992. C. Palencia and I. Alonso-Mallo, “Abstract initial boundary value problems,” Proc. R. Soc. Edinb., Sect. A., vol. 124, pp. 879–908, 1994. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | f8c430b4-d9ae-43f7-96c3-01ae7fd35912 | |
| relation.isAuthorOfPublication.latestForDiscovery | f8c430b4-d9ae-43f7-96c3-01ae7fd35912 |
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