Abstract: | A method for inverting the Laplace transform based on expanding the original in Laguerre polynomials as $ f(t) = \sum\limits_{k = 0}^\infty {a_k L_k (bt)} $ is suggested. The representation of the Laguerre series by a linear-fractional mapping is reduced to a power series of the form $ \sum\nolimits_{k = 0}^\infty {a_k z^k } A method for inverting the Laplace transform based on expanding the original in Laguerre polynomials as is suggested. The representation of the Laguerre series by a linear-fractional mapping is reduced to a power series of the
form , which is summed by the well-known Euler-Knopp method. The summation parameter is chosen in the complex plane so that the
new expansion of the original corresponding to the Euler-Knopp transformation converge at a maximum rate. On the basis of geometric representations,
the influence of the requirement that the Euler-Knopp transformation must be regular on the choice of the summation parameter
is discussed. Numerical experiments are performed, which demonstrate the high efficiency of the method of choosing a complex
parameter suggested in this paper.
Original Russian Text ? M.M. Kabardov, 2008, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika,
Mekhanika, Astronomiya, 2008, No. 4, pp. 84–89. |