Applications of Lie Groups and Gauge Functions to the Construction of Exact Difference Equations for Initial and Two-Point Boundary Value Problems

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New methods are developed to construct exact difference equations from which numerical solutions of both initial value problems and two-point boundary value problems involving first and second order ordinary differential equations can be computed. These methods are based upon the transformation theory of differential equations and require the identification of symmetry properties of the differential equations. The concept of the divergence-invariance of a variational principle is also applied to the construction of difference equations. It is shown how first and second order ordinary differential equations that admit groups of point transformations can be integrated numerically by constructing any number of ... continued below

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41 pages

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Axford, R. August 2, 2002.

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New methods are developed to construct exact difference equations from which numerical solutions of both initial value problems and two-point boundary value problems involving first and second order ordinary differential equations can be computed. These methods are based upon the transformation theory of differential equations and require the identification of symmetry properties of the differential equations. The concept of the divergence-invariance of a variational principle is also applied to the construction of difference equations. It is shown how first and second order ordinary differential equations that admit groups of point transformations can be integrated numerically by constructing any number of exact difference equations.

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41 pages

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OSTI as DE00810261

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  • Other Information: PBD: 2 Aug 2002

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  • Report No.: LA-13978
  • Grant Number: W-7405-ENG-36
  • DOI: 10.2172/810261 | External Link
  • Office of Scientific & Technical Information Report Number: 810261
  • Archival Resource Key: ark:/67531/metadc738902

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  • August 2, 2002

Added to The UNT Digital Library

  • Oct. 18, 2015, 6:40 p.m.

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  • March 11, 2016, 12:50 p.m.

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Axford, R. Applications of Lie Groups and Gauge Functions to the Construction of Exact Difference Equations for Initial and Two-Point Boundary Value Problems, report, August 2, 2002; New Mexico. (digital.library.unt.edu/ark:/67531/metadc738902/: accessed August 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.