A variable step method for the numerical integration of the one-dimensional Schrödinger equation

Raptis, AD; Cash, JR

dc.contributor.author	Raptis, AD	en
dc.contributor.author	Cash, JR	en
dc.date.accessioned	2014-03-01T01:06:23Z
dc.date.available	2014-03-01T01:06:23Z
dc.date.issued	1985	en
dc.identifier.issn	0010-4655	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9341
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0001752844&partnerID=40&md5=932a4fd644c94b73813515faa4c2a890	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Physics, Mathematical	en
dc.title	A variable step method for the numerical integration of the one-dimensional Schrödinger equation	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1985	en
heal.abstract	Most numerical methods which have been proposed for the approximate integration of the one-dimensional Schrödinger equation use a fixed step length of integration. Such an approach can of course result in gross inefficiency since the small step length which must normally be used in the initial part of the range of integration to obtain the desired accuracy must then be used throughout the integration. In this paper we consider the method of embedding, which is widely used with explicit Runge-Kutta methods for the solution of first order initial value problems, for use with the special formulae used to integrate the Schrödinger equation. By adopting this technique we have available at each step an estimate of the local truncation error and this estimate can be used to automatically control the step length of integration. Also considered is the problem of estimating the global truncation error at the end of the range of integration. The power of the approaches considered is illustrated by means of some numerical examples. © 1985.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Computer Physics Communications	en
dc.identifier.isi	ISI:A1985AKK1600001	en
dc.identifier.volume	36	en
dc.identifier.issue	2	en
dc.identifier.spage	113	en
dc.identifier.epage	119	en