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A Matrix-Vector Operation-Based Numerical Solution Method for Linear m-th Order Ordinary DifferentialEquations: Application to Engineering Problems
Vienna University of Technology. (Institute for Mechanics of Materials and Structures)
Linnaeus University, Faculty of Technology, Department of Building and Energy Technology.ORCID iD: 0000-0002-1181-8479
Vienna University of Technology. (Institute for Mechanics of Materials and Structures)
Vienna University of Technology. (Institute for Mechanics of Materials and Structures)
2013 (English)In: Advances in Applied Mathematics and Mechanics, ISSN 2070-0733, Vol. 5, no 3, 269-308 p.Article in journal (Refereed) Published
Abstract [en]

Many problems in engineering sciences can be described by linear, inhomogeneous, m-th order ordinary differential equations (ODEs) with variable coefficients. For this wide class of problems, we here present a new, simple, flexible, and robust solution method, based on piecewise exact integration of local approximation polynomials as well as on averaging local integrals. The method is designed for modern mathematical software providing efficient environments for numerical matrix-vector operation-based calculus. Based on cubic approximation polynomials, the presented method can be expected to perform (i) similar to the Runge-Kutta method, when applied to stiff initial value problems, and (ii) significantly better than the finite difference method, when applied to boundary value problems. Therefore, we use the presented method for the analysis of engineering problems including the oscillation of a modulated torsional spring pendulum, steady-state heat transfer through a cooling web, and the structural analysis of a slender tower based on second-order beam theory. Related convergence studies provide insight into the satisfying characteristics of the proposed solution scheme.

Place, publisher, year, edition, pages
2013. Vol. 5, no 3, 269-308 p.
Keyword [en]
Numerical integration, polynomial approximation, ODE, variable coefficients, initial conditions, boundary conditions, stiff equation.
National Category
Computational Mathematics Computer Engineering
Research subject
Technology (byts ev till Engineering), Civil engineering
Identifiers
URN: urn:nbn:se:lnu:diva-25623DOI: 10.4208/aamm.12-m1211ISI: 000322500200001OAI: oai:DiVA.org:lnu-25623DiVA: diva2:621100
Available from: 2013-05-13 Created: 2013-05-13 Last updated: 2015-09-28Bibliographically approved

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Dorn, Michael
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf