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Multiscale timestepping technique for ODEs and PDEs
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2014 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Tidsstegning med flera skalor för ODE och PDE (Swedish)
Abstract [en]

The focus of this thesis is to find efficient ways of solving certain types of ODEs and PDEs. We have implemented a time upscaling method called Multiscale timestepping technique for this problems. In this method discretization of PDEs are transformed into wavelet basis, which divides the solution and the discretized differential operator into coarse scales and fine scales. Larger time steps are then used for solving the fine scale elements. In numerical experiments we show that the accuracy of the solution is maintained but the computational cost is significantly reduced compared to standard methods.

Abstract [sv]

Denna uppsats behandlar effektiva metoder för att lösa vissa typer av ODE och PDE. Vi har implementerat en metod för tidsuppskaling som är baserad på tidsstegning med flera skalor. Metoden utgår från en vanlig rumsdiskretisering av en PDE. Den transformeras till en wavelet-bas som delar upp lösningen och den diskretiserade differentialoperatorn i grova och fina skalor. Stora tidssteg används sedan för att approximera de element som motsvarar fina skalor. I numeriska experiment visar vi att noggrannheten i lösningen bibehålls, men att beräkningskostnaden jämfört med standardmetoder blir betydligt mindre.

Place, publisher, year, edition, pages
TRITA-MAT-E, 2014:40
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-148167OAI: diva2:735913
Subject / course
Scientific Computing
Educational program
Master of Science - Scientific Computing
Available from: 2014-08-04 Created: 2014-08-04 Last updated: 2014-08-04Bibliographically approved

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Numerical Analysis, NA
Computational Mathematics

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