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Error analysis of finite difference schemes applied to hyperbolic initial-boundary value problems

Author: Gunilla Sk├Âllermo
Journal: Math. Comp. 33 (1979), 11-35
MSC: Primary 65N15
MathSciNet review: 514808
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Abstract: A technique for the complete error analysis of finite difference schemes for hyperbolic initial boundary value problems is developed. The error analysis is split into subproblems so that different boundary approximations or different initial approximations easily can be compared for a given interior scheme. The steps of the theoretical analysis are demonstrated on the leapfrog scheme for a simple model equation. The technique is applied to several choices of initial approximations and boundary conditions for leapfrog with second and fourth order accuracy in space. A comparison with two implicit schemes is also made. The theoretical error estimates are shown to agree very well with computational results.

References [Enhancements On Off] (What's this?)

  • [1] T. ELVIUS & A. SUNDSTRÖM, "Computationally efficient schemes and boundary conditions for a fine-mesh barotropic model based on the shallow-water equations," Tellus, v. 25, 1973, pp. 132-156.
  • [2] B. GUSTAFSSON, "The convergence rate for difference approximations to mixed initial boundary value problems," Math. Comp., v. 29, 1975, pp. 396-406. MR 0386296 (52:7154)
  • [3] B. GUSTAFSSON, H.-O. KREISS & A. SUNDSTRÖM, "Stability theory of difference approximations for mixed initial boundary value problems. II," Math. Comp., v. 26, 1972, pp. 649-686. MR 0341888 (49:6634)
  • [4] H.-O. KREISS & J. OLIGER, "Comparison of accurate methods for the integration of hyperbolic equations," Tellus, v. 24, 1972, pp. 199-215. MR 0319382 (47:7926)
  • [5] J. OLIGER, "Fourth order difference methods for the initial boundary value problem for hyperbolic equations," Math. Comp., v. 28, 1974, pp. 15-25. MR 0359344 (50:11798)
  • [6] G. SKÖLLERMO, How the Boundary Conditions Affect the Stability and Accuracy of Some Implicit Methods for Hyperbolic Equations, Report No. 62, Dept. of Comput. Sci., Uppsala University, 1975.
  • [7] B. SWARTZ & B. WENDROFF, "The relative efficiency of finite difference and finite element methods. I: Hyperbolic problems and splines," SIAM J. Numer. Anal., v. 11, 1974, pp. 979-993. MR 0362952 (50:15390)

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Keywords: Error analysis, mixed initial boundary value problem
Article copyright: © Copyright 1979 American Mathematical Society

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