Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations

Sharefa M. Asiri, Taous-Meriem Laleg-Kirati

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In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of the modulating functions-based solution is proved. The wave and the fifth-order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.
Original languageEnglish (US)
Pages (from-to)1191-1215
Number of pages25
JournalInverse Problems in Science and Engineering
Issue number8
StatePublished - Oct 20 2016

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