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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2005, Volume 45, Number 10, Pages 1848–1859
(Mi zvmmf585)
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This article is cited in 7 scientific papers (total in 7 papers)
Projection difference scheme for a parabolic functional differential equation with two-dimensional transformation of arguments
A. V. Razgulin Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
Abstract:
A nonlinear parabolic functional differential equation with the functional part containing a generalized superposition of the unknown solution and a transformation of the two-dimensional spatial argument is considered. A projection difference scheme for the approximation of the initial Dirichlet boundary value problem in a rectangle is proposed for a wide class of measurable, including noninvertible, transformations. An estimate of the rate of convergence to the generalized solutions of the initial problem of order O(τ1/4−γ+h1/2−2γ) in the norm L2(Q) without a priori assumptions on the invertibility of the transformation and without any mesh size matching is obtained.
Received: 24.05.2005
Citation:
A. V. Razgulin, “Projection difference scheme for a parabolic functional differential equation with two-dimensional transformation of arguments”, Zh. Vychisl. Mat. Mat. Fiz., 45:10 (2005), 1848–1859; Comput. Math. Math. Phys., 45:10 (2005), 1780–1791
Linking options:
https://www.mathnet.ru/eng/zvmmf585 https://www.mathnet.ru/eng/zvmmf/v45/i10/p1848
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