184,536 research outputs found
Block Method for SolvingState-Space Equations of Linear Continuous-Time Control Systems
This paper presents a newly developed method with new algorithms to find the numerical solution of nth-order state-space equations (SSE) of linear continuous-time control system by using block method. The algorithms have been written in Matlab language. The state-space equation is the modern representation to the analysis of continuous-time system. It was treated numerically to the single-input-single-output (SISO) systems as well as multiple-input-multiple-output (MIMO) systems by using fourth-order-six-steps block method. We show that it is possible to find the output values of the state-space method using block method. Comparison between the numerical and exact results has been given for some numerical examples for solving different types of state-space equations using block method for conciliated the accuracy of the results of this method
Block Method for SolvingState-Space Equations of Linear Continuous-Time Control Systems
This paper presents a newly developed method with new algorithms to find the numerical solution of nth-order state-space equations (SSE) of linear continuous-time control system by using block method. The algorithms have been written in Matlab language. The state-space equation is the modern representation to the analysis of continuous-time system. It was treated numerically to the single-input-single-output (SISO) systems as well as multiple-input-multiple-output (MIMO) systems by using fourth-order-six-steps block method. We show that it is possible to find the output values of the state-space method using block method. Comparison between the numerical and exact results has been given for some numerical examples for solving different types of state-space equations using block method for conciliated the accuracy of the results of this method
On the performance of a cavity method based algorithm for the Prize-Collecting Steiner Tree Problem on graphs
We study the behavior of an algorithm derived from the cavity method for the
Prize-Collecting Steiner Tree (PCST) problem on graphs. The algorithm is based
on the zero temperature limit of the cavity equations and as such is formally
simple (a fixed point equation resolved by iteration) and distributed
(parallelizable). We provide a detailed comparison with state-of-the-art
algorithms on a wide range of existing benchmarks networks and random graphs.
Specifically, we consider an enhanced derivative of the Goemans-Williamson
heuristics and the DHEA solver, a Branch and Cut Linear/Integer Programming
based approach. The comparison shows that the cavity algorithm outperforms the
two algorithms in most large instances both in running time and quality of the
solution. Finally we prove a few optimality properties of the solutions
provided by our algorithm, including optimality under the two post-processing
procedures defined in the Goemans-Williamson derivative and global optimality
in some limit cases
A micro-macro parareal algorithm: application to singularly perturbed ordinary differential equations
We introduce a micro-macro parareal algorithm for the time-parallel
integration of multiscale-in-time systems. The algorithm first computes a
cheap, but inaccurate, solution using a coarse propagator (simulating an
approximate slow macroscopic model), which is iteratively corrected using a
fine-scale propagator (accurately simulating the full microscopic dynamics).
This correction is done in parallel over many subintervals, thereby reducing
the wall-clock time needed to obtain the solution, compared to the integration
of the full microscopic model. We provide a numerical analysis of the algorithm
for a prototypical example of a micro-macro model, namely singularly perturbed
ordinary differential equations. We show that the computed solution converges
to the full microscopic solution (when the parareal iterations proceed) only if
special care is taken during the coupling of the microscopic and macroscopic
levels of description. The convergence rate depends on the modeling error of
the approximate macroscopic model. We illustrate these results with numerical
experiments
Stochastic methods for solving high-dimensional partial differential equations
We propose algorithms for solving high-dimensional Partial Differential
Equations (PDEs) that combine a probabilistic interpretation of PDEs, through
Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and
time-integration schemes are used to estimate pointwise evaluations of the
solution of a PDE. We use a sequential control variates algorithm, where
control variates are constructed based on successive approximations of the
solution of the PDE. Two different algorithms are proposed, combining in
different ways the sequential control variates algorithm and adaptive sparse
interpolation. Numerical examples will illustrate the behavior of these
algorithms
Effects of discrete energy and helicity conservation in numerical simulations of helical turbulence
Helicity is the scalar product between velocity and vorticity and, just like
energy, its integral is an in-viscid invariant of the three-dimensional
incompressible Navier-Stokes equations. However, space-and time-discretization
methods typically corrupt this property, leading to violation of the inviscid
conservation principles. This work investigates the discrete helicity
conservation properties of spectral and finite-differencing methods, in
relation to the form employed for the convective term. Effects due to
Runge-Kutta time-advancement schemes are also taken into consideration in the
analysis. The theoretical results are proved against inviscid numerical
simulations, while a scale-dependent analysis of energy, helicity and their
non-linear transfers is performed to further characterize the discretization
errors of the different forms in forced helical turbulence simulations
Can Computer Algebra be Liberated from its Algebraic Yoke ?
So far, the scope of computer algebra has been needlessly restricted to exact
algebraic methods. Its possible extension to approximate analytical methods is
discussed. The entangled roles of functional analysis and symbolic programming,
especially the functional and transformational paradigms, are put forward. In
the future, algebraic algorithms could constitute the core of extended symbolic
manipulation systems including primitives for symbolic approximations.Comment: 8 pages, 2-column presentation, 2 figure
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