Laguerre polynomials and the inverse Laplace transform using discrete data

• Published in: Journal of mathematical analysis and applications Vol. 337; no. 2; pp. 1302 - 1314
• Main Authors: Lien, Tran Ngoc, Trong, Dang Duc, Dinh, Alain Pham Ngoc
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 2008; Elsevier
• Subjects: Analysis of PDEs; Approximations and expansions; Exact sciences and technology; Ill-posed problem; Inverse Laplace transform; Lagrange polynomials; Laguerre polynomials; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Numerical linear algebra; Regularization; Sciences and techniques of general use; Special functions; Ill-posed problem; Laguerre polynomials; Regularization; Inverse Laplace transform; Lagrange polynomials; Approximation; Error estimation; Laguerre polynomial; Regularization method; Interpolation; Mathematical analysis; Ill posed problem; Laplace transformation; Application; ill-posed problem; regularization
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2007.04.066

We consider the problem of finding a function defined on
(
0
,
∞
)
from a countable set of values of its Laplace transform. The problem is severely ill-posed. We shall use the expansion of the function in a series of Laguerre polynomials to convert the problem in an analytic interpolation problem. Then, using the coefficients of Lagrange polynomials we shall construct a stable approximation solution. Error estimate is given. Numerical results are produced.