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Projection–difference method for controlled Fourier filtering

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A projection–difference method is developed for approximating controlled Fourier filtering for quasilinear parabolic functional-differential equations. The method relies on a projection–difference scheme (PDS) for the approximation of the differential problem and derives a O(τ1/2 + h) bound on the rate of convergence of PDS in the weighted energy norm without prior assumptions of additional smoothness of the generalized solutions. The PDS leads to a natural approximation of the objective functional in the optimal Fourier filtering problem. A bound of the same order is obtained for the rate of convergence in the functional of the problems approximating the Fourier filter control problem.

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  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    A. V. Razgulin

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  1. A. V. Razgulin
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Correspondence to A. V. Razgulin.

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Translated from Prikladnaya Matematika i Informatika, No. 36, pp. 74–90, 2010.

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Razgulin, A.V. Projection–difference method for controlled Fourier filtering. Comput Math Model 23, 56–71 (2012). https://doi.org/10.1007/s10598-012-9118-1

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