dc.contributor.author Markakis, C en_US dc.contributor.author Barack, L en_US dc.date.accessioned 2018-11-29T11:51:25Z dc.date.submitted 2018-11-19T16:10:56.933Z dc.identifier.uri http://qmro.qmul.ac.uk/xmlui/handle/123456789/53420 dc.description 9 pages, 5 figures dc.description 9 pages, 5 figures en_US dc.description 9 pages, 5 figures en_US dc.description.abstract High order finite-difference or spectral methods are typically problematic in approximating a function with a jump discontinuity. Some common remedies come with a cost in accuracy near discontinuities, or in computational cost, or in complexity of implementation. However, for certain classes of problems involving piecewise analytic functions, the jump in the function and its derivatives are known or easy to compute. We show that high-order or spectral accuracy can then be recovered by simply adding to the Lagrange interpolation formula a linear combination of the jumps. Discretizations developed for smooth problems are thus easily extended to nonsmooth problems. Furthermore, in the context of one-dimensional finite-difference or pseudospectral discretizations, numerical integration and differentiation amount to matrix multiplication. We construct the matrices for such operations, in the presence of known discontinuities, by operating on the corrected Lagrange formula. In a method-of-lines framework, this provides a simple and efficient way to obtain solutions with moving discontinuities to evolution partial differential equations. en_US dc.subject math.NA en_US dc.subject math.NA en_US dc.subject gr-qc en_US dc.title High-order difference and pseudospectral methods for discontinuous problems en_US dc.type Article dc.rights.holder © The Author(s) 2014 pubs.author-url http://arxiv.org/abs/1406.4865v1 en_US pubs.notes No embargo en_US
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