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

Sköllermo, Gunilla

doi:10.1090/S0025-5718-1979-0514808-2

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

Author: Gunilla Sköllermo
Journal: Math. Comp. 33 (1979), 11-35
MSC: Primary 65N15
DOI: https://doi.org/10.1090/S0025-5718-1979-0514808-2
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.

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