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


Pektas B.

MATHEMATICAL AND COMPUTER MODELLING, cilt.50, ss.631-643, 2009 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 50
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1016/j.mcm.2009.01.004
  • Dergi Adı: MATHEMATICAL AND COMPUTER MODELLING
  • Sayfa Sayıları: ss.631-643

Özet

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.