Issues of Patankar's numerical scheme stability

Numerical Solution of Parabolized Stability Equations Using Super Compact Scheme

Survey of numerical stability issues in convergence acceleration

A cardinal issue that arises in application of convergence acceleration (extrapolation) methods is that of numerical stability (rather lack of it) in floating-point arithmetic. This issue turns out to be critical because numerical instability is inherent, even built in, when convergence acceleration methods are applied to many sequences that occur commonly in practice. It is encountered, for ex...

Numerical stability issues of the conventional recursive least squares algorithm

The continuous use of adaptive algorithms is strongly dependent on their behavior in finite-precision environments. We study the nonlinear round-off error accumulation system of the conventional RLS algorithm and we derive bounds for the relative precision of the computations and the accumulated round-off error, which guarantee the numerical stability of the finite-precision implementation of t...

Numerical Stability Analysis of the Euler Scheme for BSDEs

In this paper, we study the qualitative behaviour of approximation schemes for Backward Stochastic Differential Equations (BSDEs) by introducing a new notion of numerical stability. For the Euler scheme, we provide sufficient conditions in the one-dimensional and multidimensional case to guarantee the numerical stability. We then perform a classical Von Neumann stability analysis in the case of...

Numerical Issues for StochasticAutomata

In this paper we consider some numerical issues in computing solutions to networks of stochastic automata (SAN). In particular our concern is with keeping the amount of computation per iteration to a minimum, since iterative methods appear to be the most eeective in determining numerical solutions. In a previous paper we presented complexity results concerning the vector-descriptor multiplicati...