Discrete Dynamic Equations Research Articles

Two adaptively stepped monotone algorithms for solving discounted dynamic programming equations

Two adaptively stepped monotone algorithms for solving discrete dynamic programming equations (DPE) for discounted Markov decision processes are introduced. They are based on, and improve two existing algorithms of the author by adopting an extra line search procedure. The new algorithms remain convergent.

Discrete mechanics and its application to the solution of the n-body problem

A theory of discrete mechanics is developed based on the results of D. Greenspan. Discrete dynamical equations in an inertial frame, in a coordinate system related to some material point, and in a rotating frame are given and the consistency, stability, and convergence of the methods are studied and some numerical examples presented.

Unconditionally stable element-by-element algorithms for dynamic problems

A collection of results is presented regarding the consistency, stability and accuracy of operator split methods and product formula algorithms for general nonlinear equations of evolution. These results are then applied to the structural dynamics problem. The basic idea is to exploit an element-by-element additive decomposition of a particular form of the discrete dynamic equations resulting from a finite element discretization. It is shown that such a particular form of the discrete dynamic equations is obtained when velocity and stress are taken as unknowns. By applying the general product formula technique to the element-by-element decomposition, unconditionally stable algorithms are obtained that involve only element coefficient matrices. The storage requirements and operation counts are comparable to those of explicit methods. The method places no restriction on the topology of the finite element mesh.

Discrete dynamical equations in minkowski space

Discrete difference equations in Minkowski space are obtained and the discrete Minkowski force is shown to be a four-vector. A transformation from a discrete dynamical equation in Minkowski space to a Lorentz-invariant difference equation in one-dimensional space is given.

On-Line Tracking of Six Orbital Elements of a Thrust Maneuvering Space Vehicle

Abstract : The problem of on-line tracking of the state variables of a thrust maneuvering space vehicle in three dimensional space described by non-linear discrete dynamical and measurement equations is studied for several different estimation schemes. A second order filtering relation is derived for a discrete non-linear plant which adds bias correction terms to the quasilinear filter. The rapid estimation scheme for a nonlinear system is employed both to provide the starting algorithm and whenever the state jump is detected. The digital computer evaluation indicates that the estimates of the states by the combination of a second order filter with the rapid estimation scheme is superior to the results obtained from quasilinear filtering techniques for the application of tracking the thrust maneuvering space vehicle. (Author)