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PGSCM: A family of -stable Boundary Value Methods for second-order initial value problems
- Source :
-
Journal of Computational & Applied Mathematics . Oct2012, Vol. 236 Issue 16, p3857-3868. 12p. - Publication Year :
- 2012
-
Abstract
- Abstract: In this paper, we introduce a family of Linear Multistep Methods used as Boundary Value Methods for the numerical solution of initial value problems for second order ordinary differential equations of special type. We rigorously prove that these schemes are -stable, in a generalized sense, of arbitrarily high order. This overcomes the barrier that Lambert and Watson established in Lambert and Watson (1976) on Linear Multistep Methods used in the classic way; that is as Initial Value Methods. We call the new methods PGSCMs, an acronym for -stable Generalized Störmer-Cowell Methods. Numerical illustrations which confirm the theoretical results of the paper are finally given. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 236
- Issue :
- 16
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 76313194
- Full Text :
- https://doi.org/10.1016/j.cam.2012.03.024