Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8901112 | Applied Mathematics and Computation | 2018 | 9 Pages |
Abstract
A procedure for computing the inverse Laplace transform of real data is obtained by using a Bessel-type quadrature which is given in terms of Laguerre polynomials LN(α)(x) and their zeros. This quadrature yields a very simple matrix expression for the Laplace transform g(s) of a function f(t) which can be inverted for real values of s. We show in this paper that the inherent instability of this inversion formula can be controlled by selecting a proper set of the parameters involved in the procedure instead of using standard regularization methods. We demonstrate how this inversion method is particularly well suited to solve problems of the form Lâ1[sg(s);t]=fâ²(t)+f(0)δ(t). As an application of this procedure, numerical solutions of a fractional differential equation modeling subdiffusion are obtained and a mean-square displacement law is numerically found.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Rafael G. Campos, Adolfo Huet,