CONSERVATIVE, HIGH-ORDER NUMERICAL SCHEMES FOR THE GENERALIZED KORTEWEG-DE VRIES EQUATION

BONA, JL; DOUGALIS, VA; KARAKASHIAN, OA; MCKINNEY, WR

dc.contributor.author	BONA, JL	en
dc.contributor.author	DOUGALIS, VA	en
dc.contributor.author	KARAKASHIAN, OA	en
dc.contributor.author	MCKINNEY, WR	en
dc.date.accessioned	2014-03-01T01:43:50Z
dc.date.available	2014-03-01T01:43:50Z
dc.date.issued	1995	en
dc.identifier.issn	0962-8428	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/24220
dc.subject.classification	Multidisciplinary Sciences	en
dc.subject.other	SOLITARY-WAVE SOLUTIONS	en
dc.subject.other	DISCRETE GALERKIN METHODS	en
dc.subject.other	DEVRIES EQUATION	en
dc.subject.other	MODEL-EQUATIONS	en
dc.subject.other	WATER-WAVES	en
dc.subject.other	LONG WAVES	en
dc.subject.other	RUNGE-KUTTA	en
dc.subject.other	STABILITY	en
dc.subject.other	APPROXIMATIONS	en
dc.subject.other	INSTABILITY	en
dc.title	CONSERVATIVE, HIGH-ORDER NUMERICAL SCHEMES FOR THE GENERALIZED KORTEWEG-DE VRIES EQUATION	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1995	en
heal.abstract	A class of fully discrete schemes for the numerical simulation of solutions of the periodic initial-value problem for a class of generalized Korteweg-de Vries equations is analysed, implemented and tested. These schemes may have arbitrarily high order in both the spatial and the temporal variable, but at the same time they feature weak theoretical stability limitations. The spatial discretization is effected using smooth splines of quadratic or higher degree, while the temporal discretization is a multi-stage, implicit, Runge-Kutta method. A proof is presented showing convergence of the numerical approximations to the true solution of the initial-value problem in the limit of vanishing spatial and temporal discretization. In addition, a careful analysis of the efficiency of particular versions of our schemes is given. The information thus gleaned is used in the investigation of the instability of the solitary-wave solutions of a certain class of these equations.	en
heal.publisher	ROYAL SOC LONDON	en
heal.journalName	PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES	en
dc.identifier.isi	ISI:A1995QW32000004	en
dc.identifier.volume	351	en
dc.identifier.issue	1695	en
dc.identifier.spage	107	en
dc.identifier.epage	164	en