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dc.contributor.authorChowdhury, Indranil
dc.contributor.authorJakobsen, Espen Robstad
dc.date.accessioned2024-09-18T08:18:08Z
dc.date.available2024-09-18T08:18:08Z
dc.date.created2024-09-16T08:45:08Z
dc.date.issued2024
dc.identifier.citationIMA Journal of Numerical Analysis. 2024, 1-40en_US
dc.identifier.issn0272-4979
dc.identifier.urihttps://hdl.handle.net/11250/3152928
dc.description.abstractWe prove precise rates of convergence for monotone approximation schemes of fractional and nonlocal Hamilton–Jacobi–Bellman equations. We consider diffusion-corrected difference-quadrature schemes from the literature and new approximations based on powers of discrete Laplacians, approximations that are (formally) fractional order and second-order methods. It is well known in numerical analysis that convergence rates depend on the regularity of solutions, and here we consider cases with varying solution regularity: (i) strongly degenerate problems with Lipschitz solutions and (ii) weakly nondegenerate problems where we show that solutions have bounded fractional derivatives of order σ ∈ (1,2).Our main results are optimal error estimates with convergence rates that capture precisely both the fractional order of the schemes andthefractional regularity of the solutions. For strongly degenerate equations, these rates improve earlier results. For weakly nondegenerate problems of order greater than one, the results are new. Here we show improved rates compared to the strongly degenerate case, rates that are always better than Oh1 2 .en_US
dc.language.isoengen_US
dc.publisherOxford University Pressen_US
dc.relation.urihttps://arxiv.org/abs/2308.16434
dc.titlePrecise Error Bounds for Numerical Approximations of Fractional HJB Equationsen_US
dc.title.alternativePrecise Error Bounds for Numerical Approximations of Fractional HJB Equationsen_US
dc.typeJournal articleen_US
dc.description.versionsubmittedVersionen_US
dc.source.pagenumber1-40en_US
dc.source.journalIMA Journal of Numerical Analysisen_US
dc.identifier.doi10.1093/imanum/drae030
dc.identifier.cristin2296605
dc.relation.projectNorges forskningsråd: 325114en_US
cristin.ispublishedtrue
cristin.fulltextpreprint
cristin.qualitycode2


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