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Eigenvalue analysis for summation-by-parts finite difference time discretizations
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-5555-9544
2020 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 58, no 2, p. 907-928Article in journal (Refereed) Published
Abstract [en]

Diagonal norm finite difference based time integration methods in summation-by-parts form are investigated. The second, fourth, and sixth order accurate discretizations are proven to have eigenvalues with strictly positive real parts. This leads to provably invertible fully discrete approximations of initial boundary value problems. Our findings also allow us to conclude that the Runge--Kutta methods based on second, fourth, and sixth order summation-by-parts finite difference time discretizations automatically satisfy previously unreported stability properties. The procedure outlined in this article can be extended to even higher order summation-by-parts approximations with repeating stencil.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2020. Vol. 58, no 2, p. 907-928
Keywords [en]
time integration; initial value problem; summation-by-parts operators; finite difference methods; eigenvalue problem
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-164555DOI: 10.1137/19M1256294OAI: oai:DiVA.org:liu-164555DiVA, id: diva2:1416555
Available from: 2020-03-24 Created: 2020-03-24 Last updated: 2020-03-31

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Nordström, JanRuggiu, Andrea Alessandro

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1819202122232421 of 122
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