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We employ a semi-implicit approach that couples the moving mesh equation to an efficient, explicit solver for the physical PDE, with the resulting scheme behaving in practice as a two-step predictor-corrector method. In comparison with computations on a fixed, uniform mesh, our method exhibits more accurate resolution of discontinuities for a similar level of computational work.<\/jats:p>","DOI":"10.1137\/s1064827599364428","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1791-1813","source":"Crossref","is-referenced-by-count":88,"title":["A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws"],"prefix":"10.1137","volume":"22","author":[{"given":"John M.","family":"Stockie","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John A.","family":"Mackenzie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert D.","family":"Russell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"G. Beckett and J. A. Mackenzie,\n                      On a uniformly accurate finite difference approximation of a singularly perturbed reaction\u2010diffusion problem using grid equidistribution\n                      , J. Comput. Appl. Math, to appear."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(83)90008-6"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997315974"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(93)90010-O"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594272025"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6151"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597327656"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759426955X"},{"key":"R9","unstructured":"J. Chen,\n                      Numerical Study of Blowup Problems and Conservation Laws with Moving Mesh Methods\n                      , Master\u2019s thesis, Simon Fraser University, Burnaby, British Columbia, Canada, 1996."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/0915050"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90161-6"},{"key":"R12","doi-asserted-by":"publisher","unstructured":"Kevin Farrell, Luke Drury, An explicit, adaptive grid algorithm for one\u2010dimensional initial value problems, Proceedings of the International Centre for Mathematical Sciences Conference on Grid Adaptation in Computational PDEs: Theory and Applications (Edinburgh, 1996), Vol. 26, 1998, 3\u20131210.1016\/S0168-9274(97)00076-71602808","DOI":"10.1016\/S0168-9274(97)00076-7"},{"key":"R13","unstructured":"R. Fazio and R. J. LeVeque,\n                      Moving\u2010mesh methods for one\u2010dimensional hyperbolic problems using Clawpack\n                      , ftp:\/\/amath.washington.edu\/pub\/rjl\/papers\/rf\u2010rjl:movingmesh.ps.gz, 1998."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(90)90148-T"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(81)90207-2"},{"key":"R16","first-page":"271","volume":"47","author":"Godunov S. K.","year":"1959","journal-title":"Mat. Sb.","ISSN":"https:\/\/id.crossref.org\/issn\/0368-8666","issn-type":"print"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(83)90066-9"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1006\/JCPH.1994.1135"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(95)00119-0"},{"key":"R20","unstructured":"R. J. LeVeque,\n                      Clawpack\u2013A software package for solving multidimensional conservation laws\n                      , in Hyperbolic Problems: Theory, Numerics, Applications, World Scientific Publishing, River Edge, NJ, 1996, pp. 188\u2013197."},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.5603"},{"key":"R22","unstructured":"S. Li,\n                      Adaptive Methods and Software for Time\u2010Dependent Partial Differential Equations\n                      , Ph.D. thesis, University of Minnesota, 1998."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596302011"},{"key":"R24","unstructured":"Linda Petzold, A description of DASSL: a differential\/algebraic system solver, IMACS Trans. Sci. Comput., I, IMACS, New Brunswick, NJ, 1983, 65\u201368751605"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(81)90128-5"},{"key":"R26","unstructured":"J. H. Smith and A. M. 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