Separation of Variables
نویسندگان
چکیده
منابع مشابه
Separation of Variables . New Trends
The review is based on the author’s papers since 1985 in which a new approach to the separation of variables (SoV) has being developed. It is argued that SoV, understood generally enough, could be the most universal tool to solve integrable models of the classical and quantum mechanics. It is shown that the standard construction of the action-angle variables from the poles of the Baker-Akhiezer...
متن کاملSeparation of Variables in Perturbed Cylinders
We study the Laplace operator subject to Dirichlet boundary conditions in a two-dimensional domain that is one-toone mapped onto a cylinder (rectangle or infinite strip). As a result of this transformation the original eigenvalue problem is reduced to an equivalent problem for an operator with variable coefficients. Taking advantage of the simple geometry we separate variables by means of the F...
متن کاملSeparation of variables via integral transformations
For a system of linear partial differential equations (LPDEs) we introduce an operator equation for auxiliary operators. These operators are used to construct a kernel of an integral transformation leading the LPDE to the separation of variables (SoV). The auxiliary operators are found for various types of the SoV including conventional SoV in the scalar second order LPDE and the SoV by the fun...
متن کاملSINC–PACK, and Separation of Variables
This talk consists of a proof of part of Stenger’s SINC-PACK computer package (an approx. 400-page tutorial + about 250 Matlab programs) that one can always achieve separation of variables when solving linear elliptic, parabolic, and hyperbolic PDE (partial differential equations) via use of Sinc methods. Some examples illustrating computer solutions via SINC-PACK will nevertheless be given in ...
متن کاملSynthesis, as Opposed to Separation, of Variables
Every applied mathematician has used separation of variables. For a given boundary value problem (BVP) in two dimensions, the starting point of this powerful method is the separation of the given PDE into two ODEs. If the spectral analysis of either of these ODEs yields an appropriate transform pair, i.e., a transform consistent with the given boundary conditions, then the given BVP can be redu...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics Supplement
سال: 1995
ISSN: 0375-9687
DOI: 10.1143/ptps.118.35