Shankar, PN (2004) *On the use of biorthogonality relations in the solution of some boundary value problems for the biharmonic equation.* Current Science, 85 (7). pp. 975-979.

## Abstract

Let a function amp;psi;(x,y), biharmonic in the semi-infinite strip {-1/2amp;lt;xamp;lt;1/2,yamp;lt;0}, be such that the function and its normal derivative vanish on the side walls x=amp;plusmn;1/2. We consider the problem of determining this function when we are given amp;psi;(x,0) and amp;nabla;lt;supgt;2lt;/supgt;amp;psi;(x,0) on the short edge y=0. First, we give a direct method of obtaining a biorthogonality relation among the eigenfunctions and then give a formal solution of the boundary value problem using this relation. Next we show that if we attempt to use this solution using a finite number of terms of the series, it is inferior to a solution where the expansion coefficients are calculating using a least squares procedure. This is a surprising result considering that for Fourier series, the Fourier coefficients are always optimal

Item Type: | Journal Article |
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Uncontrolled Keywords: | biorthogonality;Semi-infinite strip |

Subjects: | CHEMISTRY AND MATERIALS > Chemistry and Materials (General) MATHEMATICAL AND COMPUTER SCIENCES > Computer Systems |

Division/Department: | Computational and Theoretical Fluid Dynamics Division |

Depositing User: | M/S ICAST NAL |

Date Deposited: | 23 Mar 2007 |

Last Modified: | 24 May 2010 09:54 |

URI: | http://nal-ir.nal.res.in/id/eprint/4097 |

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