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• W2256319355 abstract "In this paper we consider the stability of variable step-size Runge-Kutta methods approximating bounded, stable, and time-dependent solutions of ordinary differential equation initial value problems. We use Lyapunov exponent theory to determine conditions on the maximum allowable step-size that guarantees the numerical solution of an asymptotically decaying time-dependent linear problem also decays. This result is used to justify using a one-dimensional asymptotically contracting real-valued nonautonomous linear test problem to characterize the stability of a Runge-Kutta method. The linear stability result is applied to show the stability of the numerical solution of stable nonlinear problems." @default.
• W2256319355 created "2016-06-24" @default.
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• W2256319355 date "2015-11-28" @default.
• W2256319355 modified "2023-09-27" @default.
• W2256319355 title "A Lyapunov exponents based stability theory for ODE initial value problem solvers" @default.
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• W2256319355 hasPublicationYear "2015" @default.
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