Abstract
We study an iteration method for a first-order differential-operator equation with a nonlinear operator in a separable Hilbert space. The convergence of the iterative process is proved in the strong norms. Convergence estimates are derived. We present an application of the suggested method to the solution of a model initial-boundary value problem for a fourth-order parabolic equation.
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Original Russian Text © P.V. Vinogradova, A.G. Zarubin, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 9, pp. 1238–1244.
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Vinogradova, P.V., Zarubin, A.G. On an iteration method for a nonlinear differential-operator equation. Diff Equat 50, 1225–1231 (2014). https://doi.org/10.1134/S0012266114090092
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DOI: https://doi.org/10.1134/S0012266114090092