Laguerre polynomials and the inverse Laplace transform using discrete data

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:337

Article

Lien, Tran Ngoc²  Trong, Dang Duc³  Dinh, Alain Pham Ngoc¹ 

[1] Univ Orleans, Mapmo UMR 6628, F-45067 Orleans, France

[2] Cantho Univ, Fac Sci, Can Tho, Vietnam

[3] Hochiminh City Natl Univ, Dept Math & Comp Sci, Ho Chi Minh City, Vietnam

关键词: inverse laplace transform;    Laguerre polynomials;    Lagrange polynomials;    ill-posed problem;    regularization;   

DOI  :  10.1016/j.jmaa.2007.04.066

来源: Elsevier

【 摘 要 】

We consider the problem of finding a function defined on (0, infinity) 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. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free