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

Authors:
Burhan Pektaş
Affiliations:
Department of Mathematics, Kocaeli University, Umuttepe Campus, 41380, Izmit, Kocaeli, Turkey
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

Citing 4
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Abstract

We study the backward parabolic problem related to the convection-diffusion operator Au:=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 @f(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).