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Asymptotic estimates of a projection-difference method for an operator-differential equation
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P.V. Vinogradova
Published/Copyright:
October 16, 2013
Abstract
In the current paper, we study a Petrov-Galerkin method for a Cauchy problem for an operator-differential equation with a leading self-adjoint operator A and a subordinate linear operator K(t) in a Hilbert space. Error estimates for the approximate solutions are obtained. We consider the full equation discretization based on a two-level difference scheme. New asymptotic estimates for the convergence rate of approximate solutions are obtained in uniform topology. The method is applied to the model parabolic problems.
Keywords : Cauchy problem; difference scheme; operator-differential equation; Petrov–Galerkin method; Hilbert space; orthogonal projection; convergence rate
Published Online: 2013-10-16
Published in Print: 2013-10
© 2013 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Masthead
- Analysis of the Scott–Zhang interpolation in the fractional order Sobolev spaces
- Asymptotic estimates of a projection-difference method for an operator-differential equation
- Optimal spatial error estimates for DG time discretizations
- Mixed spherical harmonic-generalized Laguerre spectral method for the Navier–Stokes equations
Keywords for this article
Cauchy problem;
difference scheme;
operator-differential equation;
Petrov–Galerkin method;
Hilbert space;
orthogonal projection;
convergence rate
Articles in the same Issue
- Masthead
- Analysis of the Scott–Zhang interpolation in the fractional order Sobolev spaces
- Asymptotic estimates of a projection-difference method for an operator-differential equation
- Optimal spatial error estimates for DG time discretizations
- Mixed spherical harmonic-generalized Laguerre spectral method for the Navier–Stokes equations
