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Spline regularization of numerical inversion of Mellin transform

  • M. Iqbal
Article
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Abstract

A method is described for inverting the Mellin transform which uses an expansion in Laguerre polynomials and converts the Mellin transform to the Laplace transform, then the Laplace transform is converted to the first kind convolution integral equation by a suitable substitution.

The integral equation so obtained is an ill-posed problem and we use the spline regularization to solve it. The performance of the method is illustrated by the inversion of the test functions available in the literature [J. Inst. Math. & Appl. 20 (1977), p. 73], [J. Math. Comp. 53 (1989), p. 589], [J. Sci. Stat. Comp. 4 (1983), p. 164]. The effectiveness of the method is shown by results obtained demonstrated by means of tables and diagrams.

Keywords

Laplace Transform Laguerre Polynomial Numerical Inversion Spline Method Convolution Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2000

Authors and Affiliations

  1. 1.Department of Mthematical SciencesKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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