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dc.contributor.authorRoe, Philip L.en_US
dc.contributor.authorArora, Mohiten_US
dc.date.accessioned2007-04-06T18:59:06Z
dc.date.available2007-04-06T18:59:06Z
dc.date.issued1993-09en_US
dc.identifier.citationRoe, Philip L.; Arora, Mohit (1993)."Characteristic-based schemes for dispersive waves I. The method of characteristics for smooth solutions." Numerical Methods for Partial Differential Equations 9(5): 459-505. <http://hdl.handle.net/2027.42/50392>en_US
dc.identifier.issn0749-159Xen_US
dc.identifier.issn1098-2426en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/50392
dc.description.abstractIn order to embark on the development of numerical schemes for stiff problems, we have studied a model of relaxing heat flow. To isolate those errors unavoidably associated with discretization, a method of characteristics is developed, containing three free parameters depending on the stiffness ratio. It is shown that such “decoupled” schemes do not take into account the interaction between the wave families and hence result in incorrect wave speeds. We also demonstrate that schemes can differ by up to two orders of magnitude in their rms errors even while maintaining second-order accuracy. We show that no method of characteristics solution can be better than second-order accurate. Next, we develop “coupled” schemes which account for the interactions, and here we obtain two additional free parameters. We demonstrate how coupling of the two wave families can be introduced in simple ways and how the results are greatly enhanced by this coupling. Finally, numerical results for several decoupled and coupled schemes are presented, and we observe that dispersion relationships can be a very useful qualitative tool for analysis of numerical algorithms for dispersive waves. © 1993 John Wiley & Sons, Inc.en_US
dc.format.extent1441830 bytes
dc.format.extent3118 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
dc.publisherJohn Wiley & Sons, Inc.en_US
dc.subject.otherMathematics and Statisticsen_US
dc.subject.otherNumerical Methodsen_US
dc.titleCharacteristic-based schemes for dispersive waves I. The method of characteristics for smooth solutionsen_US
dc.typeArticleen_US
dc.rights.robotsIndexNoFollowen_US
dc.subject.hlbsecondlevelMathematicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumThe University of Michigan, Ann Arbor, Michigan 48109-2140en_US
dc.contributor.affiliationumThe University of Michigan, Ann Arbor, Michigan 48109-2140en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/50392/1/1690090502_ftp.pdfen_US
dc.identifier.doihttp://dx.doi.org/10.1002/num.1690090502en_US
dc.identifier.sourceNumerical Methods for Partial Differential Equationsen_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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