116 research outputs found
Parallel Factorizations in Numerical Analysis
In this paper we review the parallel solution of sparse linear systems,
usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is
based on the concept of parallel factorization of a (block) tridiagonal matrix.
This allows to obtain efficient parallel extensions of many known matrix
factorizations, and to derive, as a by-product, a unifying approach to the
parallel solution of ODEs.Comment: 15 pages, 5 figure
Variable-step finite difference schemes for the solution of Sturm-Liouville problems
We discuss the solution of regular and singular Sturm-Liouville problems by
means of High Order Finite Difference Schemes. We describe a code to define a
discrete problem and its numerical solution by means of linear algebra
techniques. Different test problems are proposed to emphasize the behaviour of
the proposed algorithm
A note on the efficient implementation of implicit methods for ODEs
AbstractThe use of implicit methods for ODEs, e.g. implicit Runge-Kutta schemes, requires the solution of nonlinear systems of algebraic equations of dimension s · m, where m is the size of the continuous differential problem to be approximated. Usually, the solution of this system represents the most time-consuming section in the implementation of such methods. Consequently, the efficient solution of this section would improve their performance. In this paper, we propose a new iterative procedure to solve such equations on sequential computers
High-order finite difference schemes for the solution of second-order BVPs
AbstractWe introduce new methods in the class of boundary value methods (BVMs) to solve boundary value problems (BVPs) for a second-order ODE. These formulae correspond to the high-order generalizations of classical finite difference schemes for the first and second derivatives. In this research, we carry out the analysis of the conditioning and of the time-reversal symmetry of the discrete solution for a linear convection–diffusion ODE problem. We present numerical examples emphasizing the good convergence behavior of the new schemes. Finally, we show how these methods can be applied in several space dimensions on a uniform mesh
Considerations about the incompleteness of the Ehrenfest's theorem in quantum mechanics
We describe a study motivated by our interest to examine the incompleteness
of the Ehrenfest's theorem in quantum mechanics and to resolve a doubt
regarding whether or not the hermiticity of the hamiltonian operator is
sufficient to justify a simplification of the expression of the
macroscopic-observable time derivative that promotes the one usually found in
quantum-mechanics textbooks. The study develops by considering the simple
quantum system "particle in one-dimensional box". We propose theoretical
arguments to support the incompleteness of the Ehrenfest's theorem in the
formulation he gave, in agreement with similar findings already published by a
few authors, and corroborate them with the numerical example of an electric
charge in an electrostatic field.Comment: 28 pages, 5 figures, 1 table. To be submitted to European Journal of
Physics (https://iopscience.iop.org/journal/0143-0807
Parallel Factorizations in Numerical Analysis
In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODEIVPs or ODE-BVPs. The approach is based on the concept of parallel factorization of a (block) tridiagonal matrix. This allows to obtain efficient parallel extensions of many known matrix factorizations, and to derive, as a by-product, a unifying approach to the parallel solution of ODEs
Implementation of the PaperRank and AuthorRank indices in the Scopus database
We implement the PaperRank and AuthorRank indices introduced in [Amodio &
Brugnano, 2014] in the Scopus database, in order to highlight quantitative and
qualitative information that the bare number of citations and/or the h-index of
an author are unable to provide. In addition to this, the new indices can be
cheaply updated in Scopus, since this has a cost comparable to that of updating
the number of citations. Some examples are reported to provide insight in their
potentialities, as well as possible extensions.Comment: 19 pages, 3 figures, 4 table
Fluid statics of a self-gravitating perfect-gas isothermal sphere
We open the paper with introductory considerations describing the motivations
of our long-term research plan targeting gravitomagnetism, illustrating the
fluid-dynamics numerical test case selected for that purpose, that is, a
perfect-gas sphere contained in a solid shell located in empty space
sufficiently away from other masses, and defining the main objective of this
study: the determination of the gravitofluid-static field required as initial
field () in forthcoming fluid-dynamics calculations. The determination of
the gravitofluid-static field requires the solution of the isothermal-sphere
Lane-Emden equation. We do not follow the habitual approach of the literature
based on the prescription of the central density as boundary condition; we
impose the gravitational field at the solid-shell internal wall. As the
discourse develops, we point out differences and similarities between the
literature's and our approach. We show that the nondimensional formulation of
the problem hinges on a unique physical characteristic number that we call
gravitational number because it gauges the self-gravity effects on the gas'
fluid statics. We illustrate and discuss numerical results; some peculiarities,
such as gravitational-number upper bound and multiple solutions, lead us to
investigate the thermodynamics of the physical system, particularly entropy and
energy, and preliminarily explore whether or not thermodynamic-stability
reasons could provide justification for either selection or exclusion of
multiple solutions. We close the paper with a summary of the present study in
which we draw conclusions and describe future work.Comment: 32 pages, 26 figure
Algebraic construction and numerical behaviour of a new s-consistent difference scheme for the 2D Navier-Stokes equations
In this paper we consider a regular grid with equal spatial spacings and construct a new finite difference approximation (difference scheme) for the system of two-dimensional Navier-Stokes equations describing the unsteady motion of an incompressible viscous liquid of constant viscosity. In so doing, we use earlier constructed discretization of the system of three equations: the continuity equation and the proper Navier-Stokes equations. Then, we compute the canonical Gröbner basis form for the obtained discrete system. It gives one more difference equation which is equivalent to the pressure Poisson equation modulo difference ideal generated by the Navier-Stokes equations, and thereby comprises a new finite difference approximation (scheme). We show that the new scheme is strongly consistent. Besides, our computational experiments demonstrate much better numerical behaviour of the new scheme in comparison with the other strongly consistent schemes we constructed earlier and also with the scheme which is not strongly consistent
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