Abstract
Implicit Runge-Kutta methods, though difficult to implement, possess the strongest stability properties. This paper introduces to the theory of algebraically stable (A-contractive, B-stable) Runge-Kutta methods. These are methods for which the numerical solutions remain contractive if the (nonlinear) differential equation has contractive solutions. The proofs are sometimes omitted or sketched only, their details can be found in [13].
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© 1982 Springer-Verlag
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Hairer, E., Wanner, G. (1982). Characterization of non-linearly stable implicit Runge-Kutta methods. In: Hinze, J. (eds) Numerical Integration of Differential Equations and Large Linear Systems. Lecture Notes in Mathematics, vol 968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064889
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DOI: https://doi.org/10.1007/BFb0064889
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