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On the Construction and Comparison of Difference Schemes
Previous article Next article On the Construction and Comparison of Difference SchemesGilbert StrangGilbert Stranghttps://doi.org/10.1137/0705041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. Barkley Rosser, A Runge-Kutta for all seasons, SIAM Rev., 9 (1967), 417–452 10.1137/1009069 MR0219242 0243.65041 LinkISIGoogle Scholar[2] Robert D. Richtmyer and , K. W. Morton, Difference methods for initial-value problems, Second edition. Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967xiv+405 MR0220455 0155.47502 Google Scholar[3] Peter D. Lax and , Burton Wendroff, Difference schemes for hyperbolic equations with high order of accuracy, Comm. Pure Appl. Math., 17 (1964), 381–398 MR0170484 0233.65050 CrossrefISIGoogle Scholar[4] Samuel Z. Burstein, Numerical methods in multidimensional shocked flows, AIAA J., 2 (1964), 2111–2117 MR0180067 CrossrefGoogle Scholar[5] S. Z. Burstein, Finite-difference calculations for hydrodynamic flows containing discontinuities, J. Comp. Phys., 2 (1967), 198–222 0166.22103 Google Scholar[6] C. Berger, On the numerical range of powers of an operator, to appear Google Scholar[7] W. P. Crowley, Second-order numerical advection, J. Comp. Phys., 1 (1967), 471–484 10.1016/0021-9991(67)90053-8 0149.44403 CrossrefGoogle Scholar[8] Gilbert Strang, Accurate partial difference methods. I. Linear Cauchy problems, Arch. Rational Mech. Anal., 12 (1963), 392–402 MR0146970 0113.32303 CrossrefISIGoogle Scholar[9] A. R. Gourlay and , J. Ll. Morris, A multistep formulation of the optimized Lax-Wendroff method for nonlinear hyperbolic systems in two space variables, Math. Comp., 22 (1968), 715–719 MR0251931 0172.19904 CrossrefISIGoogle Scholar[10] Peter Lax and , Burton Wendroff, Systems of conservation laws, Comm. Pure Appl. Math., 13 (1960), 217–237 MR0120774 0152.44802 CrossrefISIGoogle Scholar[11] R. D. Richtmyer, A survey of difference methods for nonsteady fluid dynamics, Tech. Note, 63-2, National Center for Atmospheric Research, Boulder, Colorado, 1962 Google Scholar[12] Gilbert Strang, Accurate partial difference methods. II. Non-linear problems, Numer. Math., 6 (1964), 37–46 10.1007/BF01386051 MR0166942 0143.38204 CrossrefGoogle Scholar[13] Peter Henrici, Discrete variable methods in ordinary differential equat