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On the Approximation of Complicated Dynamical Behavior
 SIAM Journal on Numerical Analysis
, 1998
"... We present efficient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow to approximate SBRmeasures as well as (almost) cyclic behavior of a dynamical system. The methods are based on an appropriate discretization of ..."
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Cited by 108 (29 self)
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We present efficient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow to approximate SBRmeasures as well as (almost) cyclic behavior of a dynamical system. The methods are based on an appropriate discretization
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
, 1981
"... Several methods have been previously used to approximate free boundaries in finite difference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efficient than other metho ..."
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Cited by 603 (3 self)
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methods for treating complicated free boundary configurations. To illustrate the method, a description is given for an incompressible hydrodynamics code, SOLAVOF, that uses the VOF technique to track free fluid surfaces.
Visualizing Complicated Dynamics
 IEEE Visualization ’99 Late Breaking Hot Topics, pp. 33 – 36
, 1999
"... The temporal evolution of real world systems can mathematically be described by dynamical systems. Global, topological information on their long term behavior is given by corresponding invariant sets, which typically have a very complex structure. We describe a new, set oriented and hierarchical app ..."
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Cited by 8 (0 self)
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The temporal evolution of real world systems can mathematically be described by dynamical systems. Global, topological information on their long term behavior is given by corresponding invariant sets, which typically have a very complex structure. We describe a new, set oriented and hierarchical
Visualizing Complicated Dynamics
"... The temporal evolution of real world systems can mathematically be described by dynamical systems. Global, topological information on their long term behavior is given by corresponding invariant sets, which typically have a very complex structure. The rendering of a single, long trajectory the sta ..."
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The temporal evolution of real world systems can mathematically be described by dynamical systems. Global, topological information on their long term behavior is given by corresponding invariant sets, which typically have a very complex structure. The rendering of a single, long trajectory
Modeling and Forecasting Realized Volatility
, 2002
"... this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly rightskewed, the distributions of the logarithms of realized volatilities are a ..."
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Cited by 549 (50 self)
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are approximately Gaussian. Third, the longrun dynamics of realized logarithmic volatilities are well approximated by a fractionallyintegrated longmemory process. Motivated by the three ABDL empirical regularities, we proceed to estimate and evaluate a multivariate model for the logarithmic realized volatilities
Complicated dynamics in nonautonomous ODE's.
, 1999
"... We present a topological method for detecting complicated dynamics in nonautonomous ordinary dioeerential equations (not necesserily periodic with respect to the time variable). Our main result gives a sufficient condition for existence of a class of solutions, whose presence displays some chaotic f ..."
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Cited by 1 (1 self)
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We present a topological method for detecting complicated dynamics in nonautonomous ordinary dioeerential equations (not necesserily periodic with respect to the time variable). Our main result gives a sufficient condition for existence of a class of solutions, whose presence displays some chaotic
Efficient Implementation of Weighted ENO Schemes
, 1995
"... In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially nonoscillatory) finite difference schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L¹ norm) ENO schemes are (r +1) th order accur ..."
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Cited by 412 (38 self)
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th order WENO scheme is as fast as the 4 th order WENO scheme of Liu et al. and, both schemes are about twice as fast as the 4th order ENO schemes on vector supercomputers and as fast on serial and parallel computers. For Euler systems of gas dynamics, we suggest to compute the weights from pressure
Linear Dynamically Varying Linear Quadratic Control of Systems with Complicated Dynamics
"... Linear quadratic controllers for dynamical systems with complicated dynamics are presented. Systems with complicated dynamics are those that run over compact sets and have such features as nontrivial recurrence, periodic and aperiodic orbits. The controllers are based on modeling the nonlinear dynam ..."
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Linear quadratic controllers for dynamical systems with complicated dynamics are presented. Systems with complicated dynamics are those that run over compact sets and have such features as nontrivial recurrence, periodic and aperiodic orbits. The controllers are based on modeling the nonlinear
Results 1  10
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5,534