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Improving SIR: A Semi-Implicit Root Solver with Particular Applications to Global Solution of PDEs
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology.
2009 (English)Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

The computational core of the Generalized Weighted Residual Method (GWRM) is the Semi-implicit Root Solver (SIR), originally written in Maple.

In this paper, we improve the performance of the SIR algorithm. This improvedversion is then implemented in MATLAB. We incorporate this MATLAB version into GWRM and compare it to a similarly improved pure Maple implementation.Furthermore, Newton's method with line search (NL) is also implemented inMATLAB and compared to SIR.

In order to perform this comparison we introduce convergence maps as a new,compact, way to visualize convergence properties as we vary the initial guess. These are employed in order to compare SIR and NL in terms of stability of convergence. The tests are carried out on a predefined set of standard problems.

We conclude that the MATLAB implementation of SIR is a substantial improvement over the Maple implementation when used in GWRM. Furthermore, compared to NL, SIR is shown to have a greatly reduced sensitivity to variations in the initial guess. Conversely, NL is shown to perform slightly better when using only the initial guesses defined along with the standard problems.

This paper ends with a few suggestions on how the algorithm can be furtherimproved.

Place, publisher, year, edition, pages
2009.
Series
IT ; 09 011
Identifiers
URN: urn:nbn:se:uu:diva-103030OAI: oai:DiVA.org:uu-103030DiVA, id: diva2:217238
Presentation
(English)
Uppsok
Technology
Supervisors
Examiners
Available from: 2009-05-13 Created: 2009-05-13 Last updated: 2009-11-18Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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