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Contractivity in the numerical solution of initial value problems. (English) Zbl 0504.65030


MSC:

65J10 Numerical solutions to equations with linear operators
65L20 Stability and convergence of numerical methods for ordinary differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
34G10 Linear differential equations in abstract spaces
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References:

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[14] Rektorys, K.: Solution of mixed boundary value problems by the method of discretization in time. In: Numerische Behandlung von Differentialgleichungen Band 3. Albrecht, J., Collatz, L. (eds.). pp. 132-145, Basel: Birkhäuser Verlag 1981 · Zbl 0463.65066
[15] Rickart, C.E.: General theory of Banach algebras. New York: Van Nostrand 1960 · Zbl 0095.09702
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[17] Spijker, M.N.: Contractivity of Runge-Kutta methods. In: Numerical methods for solving stiff initial value problems. Proceedings, Oberwolfach, 28.6.?4.7.1981. Dahlquist, G., Jeltsch, R. (eds.). Institut für Geometrie und Praktische Mathematik der RWTH Aachen, Bericht Nr. 9, 1981
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