PGSCM: A family of -stable Boundary Value Methods for second-order initial value problems

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• 作者：Lidia Aceto ^{l.aceto@dma.unipi.it} ; Paolo Ghelardoni ^{ghelardoni@dma.unipi.it} ; Cecilia Magherini ; ^{cecilia.magherini@dma.unipi.it}
• 关键词：65L05 ; 65L20 ; 65L04
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2012
• 出版时间：October, 2012
• 年：2012
• 卷：236
• 期：16
• 页码：3857-3868
• 全文大小：336 K

文摘

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 St?rmer-Cowell Methods. Numerical illustrations which confirm the theoretical results of the paper are finally given.