Recovering the spatial distribution of a groundwater contaminant at a prior time: The forward collocation method

Pektas, Burhan

doi:10.1016/j.mcm.2009.01.004

Recovering the spatial distribution of a groundwater contaminant at a prior time: The forward collocation method

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Pektas B.

MATHEMATICAL AND COMPUTER MODELLING, vol.50, pp.631-643, 2009 (SCI-Expanded)

Publication Type: Article / Article
Volume: 50
Publication Date: 2009
Doi Number: 10.1016/j.mcm.2009.01.004
Journal Name: MATHEMATICAL AND COMPUTER MODELLING
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Page Numbers: pp.631-643
Kocaeli University Affiliated: No

Abstract

We study the backward parabolic problem related to the convection-diffusion operator Au :equivalent to u(t) - (D(x)u(x))(x) + (c(x)u)(x) when the diffusion coefficient D(x) may be discontinuous. The forward collocation method (FC-method) is used for numerical solution of this backward transmission problem. According to the method, we approximate the unknown function phi(x) = (u(x, t(0)) by the piecewise linear continuous, Lagrange type of basis functions. Moreover, we solve the obtained ill-conditioned system of algebraic equations by using truncated singular value decomposition (TSVD). (C) 2009 Elsevier Ltd. All rights reserved.