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High order accurate two-step approximations for hyperbolic equations. (English) Zbl 0411.65057

MSC:
65N06 Finite difference methods for boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
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References:
[1] 1. G. A. BAKER and J. H. BRAMBLE, Semidiscrete and Single Step Fully Discrete Approximations for Second Order Hyperbolic Equations, Rapport Interne No. 22, Centre de Mathématiques appliquées, École polytechnique, Palaiseau, 1977. · Zbl 0405.65057
[2] 2. G. A. BAKER and V. A. DOUGALIS, On the L x -Convergence of Approximations for Hyperbolic Equations (to appear in Math. Comp.). Zbl0454.65078 MR559193 · Zbl 0454.65078
[3] 3. G. A. BAKER, V. A. DOUGALIS and S. M. SERBIN, An Approximation Theorem for Second-Order Evolution Equations (to appear in Numer. Math.). Zbl0445.65075 MR585242 · Zbl 0445.65075
[4] 4. J. H. BRAMBLE, A. H. SCHATZ, V. THOMÉE and L. B. WAHLBIN, Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations, S.I.A.M., J. Numer. Anal., Vol. 14, 1977, pp. 218-241. Zbl0364.65084 MR448926 · Zbl 0364.65084
[5] 5. M. CROUZEIX, Sur l’approximation des équations différentielles opérationnelles linéaires par des méthodes de Runge-Kutta, Thèse, Université Paris-VI, 1975.
[6] 6. V. A. DOUGALIS, Multistep Galerkin Methods for Hyperbolic Equations, Math.Comp., Vol. 33, 1979, pp, 563-584. Zbl0417.65057 MR521277 · Zbl 0417.65057
[7] 7. T. DUPONT, L2-Estimates for Galerkin Methods for Second-Order Hyperbolic Equations, S.I.A.M., J. Numer. Anal., Vol. 1973, pp.880-889. Zbl0239.65087 MR349045 · Zbl 0239.65087
[8] 8. E. GEKELER, Linear Multistep Methods and Galerkin Procedures for Initial-Boundary Value Problems, S.I.A.M., J. Numer. Anal., Vol. 13, 1976, pp.536-548. Zbl0335.65042 MR431749 · Zbl 0335.65042
[9] 9. E. GEKELER, Galerkin-Runge-Kutta Methods and Hyperbolic Initial Boundary Value Problems, Computing, Vol. 18, 1977, pp.79-88. Zbl0348.65087 MR438739 · Zbl 0348.65087
[10] 10. S. M. SERBIN, Rational Approximations of Trigonométric Matrices with Applications to Second-Order Systems of Differential Equations, Appl. Math, and Computation, Vol. 5, 1979, pp. 75-92. Zbl0408.65047 MR516304 · Zbl 0408.65047
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