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.
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