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2009-07-01Zeitschriftenartikel DOI: 10.1515/ADVGEOM.2009.020
Application of numerical continuation to compute all solutions of semilinear elliptic equations
dc.contributor.authorAllgower, Eugene
dc.contributor.authorCruceanu, Stefan-Gicu
dc.contributor.authorTavener, Simon
dc.date.accessioned2017-06-17T09:46:34Z
dc.date.available2017-06-17T09:46:34Z
dc.date.created2010-07-01
dc.date.issued2009-07-01
dc.identifier.issn1615-7168
dc.identifier.urihttp://edoc.hu-berlin.de/18452/12572
dc.description.abstractWe adapt numerical continuation methods to compute all solutions of finite difference discretizations of nonlinear boundary value problems involving the Laplacian in two dimensions. New solutions on finer meshes are obtained from solutions on coarser meshes using a complex homotopy deformation. Two difficulties arise. First, the number of solutions typically grows with the number of mesh points and some form of filtering becomes necessary. Secondly, bifurcations may occur along homotopy paths of solutions and efficient methods to swap branches are developed when the mappings are analytic. For polynomial nonlinearities we generalize an earlier strategy for finding all solutions of two-point boundary value problems in one dimension and then introduce exclusion algorithms to extend the method to general nonlinearities.eng
dc.language.isound
dc.publisherKooperation de Gruyter
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.titleApplication of numerical continuation to compute all solutions of semilinear elliptic equations
dc.typearticle
dc.identifier.urnurn:nbn:de:kobv:11-100150542
dc.identifier.doi10.1515/ADVGEOM.2009.020
dc.identifier.doihttp://dx.doi.org/10.18452/11920
local.edoc.container-titleAdvances in Geometry
local.edoc.type-nameZeitschriftenartikel
local.edoc.container-typeperiodical
local.edoc.container-type-nameZeitschrift
local.edoc.container-publisher-namede Gruyter
local.edoc.container-volume9
local.edoc.container-issue3
local.edoc.container-year2009
local.edoc.container-firstpage371
local.edoc.container-lastpage400
dc.description.versionPeer Reviewed

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