4,404 research outputs found
A sequential regularization method for time-dependent incompressible Navier--Stokes equations
The objective of the paper is to present a method, called sequential regularization method (SRM), for the nonstationary incompressible Navier-Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs) , and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs). The SRM is a functional iterative procedure. It is proved that its convergence rate is O(ffl m ), where m is the number of the SRM iterations and ffl is the regularization parameter. The discretization and implementation issues of the method are considered. In particular, a simple explicit difference scheme is analyzed and its stability is proved under the usual step size condition of explicit schemes. It appears that the SRM formulation is new in the Navier-Stokes context. Unlike other regularizations or pseudo-compressibility methods in the Navier-Stokes context, the regularization parameter ffl in the SRM need not be very small, and the regularized..
A Note on the âConstructingâ of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence
This paper is partially supported by project ISM-4 of Department for Scientific Research,
âPaisii Hilendarskiâ University of Plovdiv.In this paper we give methodological survey of âcontemporary methodsâ for solving the nonlinear equation f(x) = 0. The reason for
this review is that many authors in present days rediscovered such classical methods. Here we develop one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence
Hydration of a B-DNA Fragment in the Method of Atom-atom Correlation Functions with the Reference Interaction Site Model Approximation
We propose an efficient numerical algorithm for solving integral equations of
the theory of liquids in the Reference Interaction Site Model (RISM)
approximation for infinitely dilute solution of macromolecules with a large
number of atoms. The algorithm is based on applying the nonstationary iterative
methods for solving systems of linear algebraic equations. We calculate the
solvent-solute atom-atom correlation functions for a fragment of the B-DNA
duplex d(GGGGG).d(CCCCC) in infinitely dilute aqueous solution. The obtained
results are compared with available experimental data and results from computer
simulations.Comment: 9 pages, RevTeX, 9 pages of ps figures, accepted for publications in
JC
A new nonlocal thermodynamical equilibrium radiative transfer method for cool stars
Context: The solution of the nonlocal thermodynamical equilibrium (non-LTE)
radiative transfer equation usually relies on stationary iterative methods,
which may falsely converge in some cases. Furthermore, these methods are often
unable to handle large-scale systems, such as molecular spectra emerging from,
for example, cool stellar atmospheres.
Aims: Our objective is to develop a new method, which aims to circumvent
these problems, using nonstationary numerical techniques and taking advantage
of parallel computers.
Methods: The technique we develop may be seen as a generalization of the
coupled escape probability method. It solves the statistical equilibrium
equations in all layers of a discretized model simultaneously. The numerical
scheme adopted is based on the generalized minimum residual method.
Result:. The code has already been applied to the special case of the water
spectrum in a red supergiant stellar atmosphere. This demonstrates the fast
convergence of this method, and opens the way to a wide variety of
astrophysical problems.Comment: 13 pages, 9 figure
Low-frequency expansion for probability amplitudes: An alternative approach to certain intramolecular dynamics problems
We present an algorithm to determine the averaged time evolution of the probability amplitude for a nonstationary state in a quantum mechanical system. The algorithm is based on a lowâfrequency expansion of the probability amplitude and is related to the generalized moment expansion method which has been applied successfully to the description of dynamic correlation functions in stochastic systems. It is shown that the proposed algorithm gives excellent results for the description of quantum beats in the time evolution of the occupation probability for a nonstationary state in model systems. The relation of the algorithm to other theoretical approaches and the relevance for the description of intramolecular energy transfer processes is discussed
Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations
A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics
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