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The dynamical functional particle method: an approach for boundary value problems
Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design. (Computational mathematics and physics)
Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design. (Computational mathematics and physics)
Mid Sweden University, Faculty of Science, Technology and Media, Department of applied science and design. (Mekanik)ORCID iD: 0000-0002-2066-5486
2012 (English)In: Journal of applied mechanics, ISSN 0021-8936, E-ISSN 1528-9036, Vol. 79, no 2, p. art. no. 021012-Article in journal (Refereed) Published
Abstract [en]

The present work is concerned with new ideas of potential value for solving differential equations. First, a brief introduction to particle methods in mechanics is made by revisiting the vibrating string. The full case of nonlinear motion is studied and the corresponding nonlinear differential equations are derived. It is suggested that the particle origin of these equations is of more general interest than usually considered. A novel possibility to develop particle methods for solving differential equations in a direct way is investigated. The dynamical functional particle method (DFPM) is developed as a solution method for boundary value problems. DFPM is based on the concept of an interaction functional as a dynamical force field acting on quasi particles. The approach is not limited to linear equations. We exemplify by applying DFPM to several linear Schrödinger type of problems as well as a nonlinear case. It is seen that DFPM performs very well in comparison with some standard numerical libraries. In all cases, the convergence rates are exponential in time. © 2012 American Society of Mechanical Engineers.

Place, publisher, year, edition, pages
2012. Vol. 79, no 2, p. art. no. 021012-
Keywords [en]
DFPM; dynamical functional particle method; interaction functional; many-particle systems; partial differential equations; particle methods; Schrödinger equation
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Identifiers
URN: urn:nbn:se:miun:diva-12267DOI: 10.1115/1.4005563ISI: 000302580000012Scopus ID: 2-s2.0-84859910326OAI: oai:DiVA.org:miun-12267DiVA, id: diva2:371883
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Accepterad för publicering.

Available from: 2010-11-23 Created: 2010-11-23 Last updated: 2017-12-12Bibliographically approved

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Edvardsson, SverkerGulliksson, MårtenPersson, Johan

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