New stability results for explicit Runge–Kutta methods
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DOI: 10.1007/s10543-019-00752-9
Abstract: The theory of polar forms of polynomials is used to provide sharp bounds on the radius of the largest possible disc (absolute stability radius), and on the length of the largest possible real interval (parabolic… read more here.
Keywords: explicit runge; stability radius; new stability; absolute stability ... See more keywords
Variational formulations for explicit Runge-Kutta Methods
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DOI: 10.1016/j.finel.2019.06.007
Abstract: Variational space-time formulations for Partial Differential Equations have been of great interest in the last decades. While it is known that implicit time marching schemes have variational structure, the Galerkin formulation of explicit methods in… read more here.
Keywords: runge kutta; time; explicit runge; kutta methods ... See more keywords
Round-Off Error and Exceptional Behavior Analysis of Explicit Runge-Kutta Methods
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DOI: 10.1109/tc.2019.2917902
Abstract: Numerical integration schemes are mandatory to understand complex behaviors of dynamical systems described by ordinary differential equations. Implementation of these numerical methods involve floating-point computations and propagation of round-off errors. This paper presents a new… read more here.
Keywords: runge kutta; kutta methods; runge; round error ... See more keywords