Construction of Difference Equations Using Lie Groups

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Description

The theory of prolongations of the generators of groups of point transformations to the grid point values of dependent variables and grid spacings is developed and applied to the construction of group invariant numerical algorithms. The concepts of invariant difference operators and generalized discrete sources are introduced for the discretization of systems of inhomogeneous differential equations and shown to produce exact difference equations. Invariant numerical flux functions are constructed from the general solutions of first order partial differential equations that come out of the evaluation of the Lie derivatives of conservation forms of difference schemes. It is demonstrated that invariant ... continued below

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Medium: P; Size: 78 pages

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Axford, R. A. August 1998.

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Description

The theory of prolongations of the generators of groups of point transformations to the grid point values of dependent variables and grid spacings is developed and applied to the construction of group invariant numerical algorithms. The concepts of invariant difference operators and generalized discrete sources are introduced for the discretization of systems of inhomogeneous differential equations and shown to produce exact difference equations. Invariant numerical flux functions are constructed from the general solutions of first order partial differential equations that come out of the evaluation of the Lie derivatives of conservation forms of difference schemes. It is demonstrated that invariant numerical flux functions with invariant flux or slope limiters can be determined to yield high resolution difference schemes. The introduction of an invariant flux or slope limiter can be done so as not to break the symmetry properties of a numerical flux-function.

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Medium: P; Size: 78 pages

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INIS; OSTI as DE00001172

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  • Other Information: PBD: 1 Aug 1998

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  • Report No.: LA-13499
  • Grant Number: W-7405-ENG-36
  • DOI: 10.2172/1172 | External Link
  • Office of Scientific & Technical Information Report Number: 1172
  • Archival Resource Key: ark:/67531/metadc624375

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  • August 1998

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  • June 16, 2015, 7:43 a.m.

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  • May 16, 2016, 11:31 a.m.

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Axford, R. A. Construction of Difference Equations Using Lie Groups, report, August 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc624375/: accessed September 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.