Kumar, Anand (1999) *Supersymmetric finite-difference formulae.* Technical Report. CMMACS/ National Aerospace Laboratories, Bangalore, India.

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## Abstract

New finite-difference formulae have been developed such that the discretisation of the Laplace operator is rotationally invariant. These formulae, referred to by supersymmetric finite-difference formulae, ensure that the mean value theorem for a harmonic function is preserved on the discretisation of the Laplace equation. Formulae in two and three dimensions have been obtained. Supersymmetric discretisation of the Laplacian in n-dimension is given. The L two and L infinity, stability limits of the heat conduction equation in n-dimension, which are 1/2n for the conventional differencing, have been shown to be 1/2 and 2 to th power of n-2 divided by 2 to the power of n-1, respectively under the supersymrnetric discretisation. Thus while the L two stability limit for the supersymmetric discretisation is dimension-independent, the L infinity, stability limit is greater than 1/4 for any n

Item Type: | Proj.Doc/Technical Report (Technical Report) |
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Uncontrolled Keywords: | Supersymmetric;Finite-difference;Discret;Stability |

Subjects: | MATHEMATICAL AND COMPUTER SCIENCES > Mathematical and Computer Scienes(General) |

Division/Department: | CSIR Centre for Mathematical Modelling and Computer Simulation |

Depositing User: | Mr. Ravikumar R |

Date Deposited: | 31 Jul 2006 |

Last Modified: | 24 May 2010 09:44 |

URI: | http://nal-ir.nal.res.in/id/eprint/1903 |

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