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Abstract
We consider two inverse problems for estimating the source coefficients q(x) and q(x, y) in the advection-dispersion equations, where the q are presumed to be continuous functions of space variables which are delineated by some physical/chemical reactions happening in the solute transportation. A Lie-group adaptive method (LGAM) is developed, which can be employed to discover q at spatially discretized points, needing merely a few measured concentration data at a terminal time t f as a target to determine a suitable value of the parameter r ∈ [0, 1] emerging in the current approach. The efficiency and accuracy of the present algorithm are verified by comparing the estimated results with some exact solutions for several examples.
Acknowledgments
The corresponding author would like to express his thanks to the National Science Council, ROC, for financial support under Grant Number NSC 100-2221-E492-018.