176 research outputs found
Discrete variable methods for delay-differential equations with threshold-type delays
AbstractWe study numerical solution of systems of delay-differential equations in which the delay function, which depends on the unknown solution, is defined implicitly by the threshold condition. We study discrete variable numerical methods for these problems and present error analysis. The global error is composed of the error of solving the differential systems, the error from the threshold conditions and the errors in delay arguments. Our theoretical analysis is confirmed by numerical experiments on threshold problems from the theory of epidemics and from population dynamics
Two-step almost collocation methods for Volterra integral equations
In this paper we construct a new class of continuous methods for Volterra integral equations.
These methods are obtained by using a collocation technique and by relaxing some of the collocation conditions in order to obtain good stability properties
Pseudospectra of waveform relaxation operators
Abstract--The performance of the waveform relaxation method for solving systems of ODEs depends largely on the choices that are made for splitting, size of time window, and preconditioning. Although it is known that superlinear convergence is obtained on finite time windows, the convergence may be slow in the first few iterations. We propose the use of pseudcepectra to analyze the convergence ratio of the first few iterations when waveform relaxation is applied to linear systems of ODEs. Through pseudcepectral radii, we can examine the effect of preconditioning and overlapping on the rate of convergence. We may also use this to estimate a suitable size of the time window. Numerical experiments performed on a system of ODEs arising from the discretization of an advection-diffusion equation confirm the validity of the obtained estimates. (~) 1998 Elsevier Science Ltd. All rights reserved
Finite-Difference and Pseudo-Sprectral Methods for the Numerical Simulations of In Vitro Human Tumor Cell Population Kinetics
Pseudo-spectral approximations are constructed for the model equations which describe the population kinetics of human tumor cells in vitro and their responses to radiotherapy or chemotherapy. These approximations are more efficient than finite-difference approximations. The spectral accuracy of the pseudo-spectral method allows us to resolve the model with a much smaller number of spatial grid-points than required for the finite-difference method to achieve comparable accuracy. This is demonstrated by numerical experiments which show a good agreement between predicted and experimental data
Spectral approximation of time windows in waveform relaxation
We establish a relationship between the spectral parameter arising in Laplace transform of the solution of a linear differential system and the time window in which this system is solved
Exploiting solar visible-range observations by inversion techniques: from flows in the solar subsurface to a flaring atmosphere
Observations of the Sun in the visible spectral range belong to standard
measurements obtained by instruments both on the ground and in the space.
Nowadays, both nearly continuous full-disc observations with medium resolution
and dedicated campaigns of high spatial, spectral and/or temporal resolution
constitute a holy grail for studies that can capture (both) the long- and
short-term changes in the dynamics and energetics of the solar atmosphere.
Observations of photospheric spectral lines allow us to estimate not only the
intensity at small regions, but also various derived data products, such as the
Doppler velocity and/or the components of the magnetic field vector. We show
that these measurements contain not only direct information about the dynamics
of solar plasmas at the surface of the Sun but also imprints of regions below
and above it. Here, we discuss two examples: First, the local time-distance
helioseismology as a tool for plasma dynamic diagnostics in the near subsurface
and second, the determination of the solar atmosphere structure during flares.
The methodology in both cases involves the technique of inverse modelling.Comment: 29 pages, 15 figures. Accepted for publication in the book "Reviews
in Frontiers of Modern Astrophysics: From Space Debris to Cosmology" (eds
Kabath, Jones and Skarka; publisher Springer Nature) funded by the European
Union Erasmus+ Strategic Partnership grant "Per Aspera Ad Astra Simul"
2017-1-CZ01-KA203-03556
Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results
The chromosphere is a thin layer of the solar atmosphere that bridges the
relatively cool photosphere and the intensely heated transition region and
corona. Compressible and incompressible waves propagating through the
chromosphere can supply significant amounts of energy to the interface region
and corona. In recent years an abundance of high-resolution observations from
state-of-the-art facilities have provided new and exciting ways of
disentangling the characteristics of oscillatory phenomena propagating through
the dynamic chromosphere. Coupled with rapid advancements in
magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly
investigate the role waves play in supplying energy to sustain chromospheric
and coronal heating. Here, we review the recent progress made in
characterising, categorising and interpreting oscillations manifesting in the
solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review
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