2,526 research outputs found
A symmetry-adapted numerical scheme for SDEs
We propose a geometric numerical analysis of SDEs admitting Lie symmetries
which allows us to individuate a symmetry adapted coordinates system where the
given SDE has notable invariant properties. An approximation scheme preserving
the symmetry properties of the equation is introduced. Our algorithmic
procedure is applied to the family of general linear SDEs for which two
theoretical estimates of the numerical forward error are established.Comment: A numerical example adde
Generalized evolutionary equations with imposed symmetries
The paper proposes an algorithm which could identify a general class of pdes
describing dynamical systems with similar symmetries. The way that will be
followed starts from a given group of symmetries, the determination of the
invariants and, then, of the compatible equations of evolution. The algorithm
will be exemplified by two classes of equations which describe the
Fokker-Planck model and the "backward" Kolgomorov one.Comment: 7th General Conference of the Balkan Physics Union, Published in AIP
Conference Proceedings, Vol 1203 (2009), 1172-117
Nonlinear Dirac and diffusion equations in 1 + 1 dimensions from stochastic considerations
We generalize the method of obtaining the fundamental linear partial
differential equations such as the diffusion and Schrodinger equation, Dirac
and telegrapher's equation from a simple stochastic consideration to arrive at
certain nonlinear form of these equations. The group classification through one
parameter group of transformation for two of these equations is also carried
out.Comment: 18 pages, Latex file, some equations corrected and group analysis in
one more case adde
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