8,501 research outputs found
Lie point symmetries of difference equations and lattices
A method is presented for finding the Lie point symmetry transformations
acting simultaneously on difference equations and lattices, while leaving the
solution set of the corresponding difference scheme invariant. The method is
applied to several examples. The found symmetry groups are used to obtain
particular solutions of differential-difference equations
Lie Symmetries and Exact Solutions of First Order Difference Schemes
We show that any first order ordinary differential equation with a known Lie
point symmetry group can be discretized into a difference scheme with the same
symmetry group. In general, the lattices are not regular ones, but must be
adapted to the symmetries considered. The invariant difference schemes can be
so chosen that their solutions coincide exactly with those of the original
differential equation.Comment: Minor changes and journal-re
Oscillations and stability of numerical solutions of the heat conduction equation
The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform
Difference schemes with point symmetries and their numerical tests
Symmetry preserving difference schemes approximating second and third order
ordinary differential equations are presented. They have the same three or
four-dimensional symmetry groups as the original differential equations. The
new difference schemes are tested as numerical methods. The obtained numerical
solutions are shown to be much more accurate than those obtained by standard
methods without an increase in cost. For an example involving a solution with a
singularity in the integration region the symmetry preserving scheme, contrary
to standard ones, provides solutions valid beyond the singular point.Comment: 26 pages 7 figure
Symmetries of differential-difference dynamical systems in a two-dimensional lattice
Classification of differential-difference equation of the form
are considered
according to their Lie point symmetry groups. The set represents the
point and its six nearest neighbors in a two-dimensional triangular
lattice. It is shown that the symmetry group can be at most 12-dimensional for
abelian symmetry algebras and 13-dimensional for nonsolvable symmetry algebras.Comment: 24 pages, 1 figur
Marginal cost-based pricing of distribution: a case study
This paper presents results of a software development project carried out by the “Electricity North West” (ENW) and “TNEI” to find economic use-of-system charges for the extra high-voltage (EHV) network. Several cost-based charging models which satisfy principles set by the Regulator, such as cost reflectivity, predictability, stability and transparency were developed. In this paper, the emphasis is put on the developed software and the comparison of nodal marginal charges obtained from the proposed pricing models
QCDF90: Lattice QCD with Fortran 90
We have used Fortran 90 to implement lattice QCD. We have designed a set of
machine independent modules that define fields (gauge, fermions, scalars,
etc...) and overloaded operators for all possible operations between fields,
matrices and numbers. With these modules it is very simple to write high-level
efficient programs for QCD simulations. To increase performances our modules
also implements assignments that do not require temporaries, and a machine
independent precision definition. We have also created a useful compression
procedure for storing the lattice configurations, and a parallel implementation
of the random generators. We have widely tested our program and modules on
several parallel and single processor supercomputers obtaining excellent
performances.Comment: LaTeX file, 8 pages, no figures. More information available at:
http://hep.bu.edu/~leviar/qcdf90.htm
The Taming of QCD by Fortran 90
We implement lattice QCD using the Fortran 90 language. We have designed
machine independent modules that define fields (gauge, fermions, scalars,
etc...) and have defined overloaded operators for all possible operations
between fields, matrices and numbers. With these modules it is very simple to
write QCD programs. We have also created a useful compression standard for
storing the lattice configurations, a parallel implementation of the random
generators, an assignment that does not require temporaries, and a machine
independent precision definition. We have tested our program on parallel and
single processor supercomputers obtaining excellent performances.Comment: Talk presented at LATTICE96 (algorithms) 3 pages, no figures, LATEX
file with ESPCRC2 style. More information available at:
http://hep.bu.edu/~leviar/qcdf90.htm
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