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<< JRScience Home   Volume 12 No.1 June 2001 << Back to Volume Home

THE NUMERICAL INVERSION OF THE LAPLACE TRANSFORM IN REPRODUCING KERNEL HILBERT SPACES

M. Iqbal

Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals,

Dhahran 31261, Saudi Arabia

Abstract: In this paper we have converted the Laplace transform into an integral equation of the first kind of convolution type, which is an ill-posed problem and used a statistical regularization method to solve it. The method is applied to three examples taken from Rodriguez and Seatzu [1993]. It gives a good approximation to the true solution and compares well with the method given by Rodriguez and Seatzu [1993]. The results are shown in the Table and the diagrams.

 

Keywords: Ill-posed problem, inversion of Laplace transform, convolution equation, cross-validation, filter function, regularization parameter.