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Eigenvalue analysis for summation-by-parts finite difference time discretizationsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2019 (English)Report (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Linköping: Linköping University Electronic Press, 2019. , p. 35
##### Series

LiTH-MAT-R, ISSN 0348-2960 ; 2019:9
##### 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-160009ISRN: LiTH-MAT-R-2019/09-SEOAI: oai:DiVA.org:liu-160009DiVA, id: diva2:1347842
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt485",{id:"formSmash:j_idt485",widgetVar:"widget_formSmash_j_idt485",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt491",{id:"formSmash:j_idt491",widgetVar:"widget_formSmash_j_idt491",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt500",{id:"formSmash:j_idt500",widgetVar:"widget_formSmash_j_idt500",multiple:true}); Available from: 2019-09-02 Created: 2019-09-02 Last updated: 2019-09-03Bibliographically approved
##### In thesis

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 second, fourth and sixth order time discretizations are stiffly accurate, strongly *S*-stable and dissipatively stable Runge-Kutta methods. The procedure outlined in this article can be extended to even higher order summation-by-parts approximations with repeating stencil.

1. Eigenvalue analysis and convergence acceleration techniques for summation-by-parts approximations$(function(){PrimeFaces.cw("OverlayPanel","overlay1348178",{id:"formSmash:j_idt795:0:j_idt800",widgetVar:"overlay1348178",target:"formSmash:j_idt795:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1315",{id:"formSmash:lower:j_idt1315",widgetVar:"widget_formSmash_lower_j_idt1315",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1316_j_idt1318",{id:"formSmash:lower:j_idt1316:j_idt1318",widgetVar:"widget_formSmash_lower_j_idt1316_j_idt1318",target:"formSmash:lower:j_idt1316:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});