Abstract:
A new approach for solution of inverse coecient problem for some types of partial dierential equations with variable coecient is considered. This approach is based on proposed by author General Ray Principle and leads to the new GR-Method, which consists in reduction of the partial dierential equation to assemblage of ordinary dierential equations using local traces for considered functions and operators. New method presents the solution of considered problems by explicit analytical formulas that use the direct and inverse Radon transform. In the case of noised input data the regularization with Recursive Spline Smoothing is used. Proposed method is realized by fast and stable algorithms and
MATLAB software, which quality is demonstrated by numerical experiments. Applications to electric tomography and mathematical simulation in creation of nano-composite materials with special heat-conductive properties are considered.
Keywords:inverse problems, PDE coecients, electric tomography.
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