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An approximation theorem for second-order evolution equations. (English) Zbl 0445.65075

MSC:
65L05 Numerical methods for initial value problems
35L20 Initial-boundary value problems for second-order hyperbolic equations
34G10 Linear differential equations in abstract spaces
65J10 Numerical solutions to equations with linear operators (do not use 65Fxx)
41A20 Approximation by rational functions
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References:
[1] Baker, G.A., Bramble, J.H.: Semidiscrete and single step fully discrete approximations for second-order hyperbolic equations. RAIRO Analyse Numérique13, 75-100 (1979) · Zbl 0405.65057
[2] Crouzeix, M.: Sur l’approximation des équations différentielles opérationelles linéaires par des méthodes de Runge-Kutta. Thèse, Université Paris VI, 1975
[3] Kre?n, S.G.: Linear differential equations in Banach space. Transl. Math. Monographs Vol.29, American Mathematical Society, Providence, R.I., 1971
[4] Serbin, S.M.: Rational approximations of trigonometric matrices with applications to second-order systems of differential equations, Appl. Math. Comput.5, 57-92 (1979) · Zbl 0408.65047 · doi:10.1016/0096-3003(79)90011-0
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