Advertisement

On Rothe and Rothe-Galerkin method for differential-operator equation

  • A. G. Zarubin
Conference paper

Abstract

Great number of papers are reduced to finding of Cauchy problem for differential-operator equation in form
$$ u'(t) + Au(t) + F(u(t)) = f(t),\quad u(0) = 0 $$
(1)
in Hilbert space H, where A is a linear and F is non-linear operators. This paper is continuation of papers [1]–[2]. Finding of approximate solution by Rothe and Rothe-Galerkin methods is reduced, unlike [2], to solving of stationary linear operator equation or to solving of linear algebraic system.

Keywords

Hilbert Space Cauchy Problem Separable Hilbert Space Linear Algebraic System Linear Hull 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A.G. Zarubin, M.P. Tiunchik, On a Rothe-Galerkin method for one class of linear non-stationary equations, Diff. Equations, V.19 (1983), pp.2141–2148.MathSciNetGoogle Scholar
  2. [2]
    A.G. Zarubin, On a convergance rate of Rothe-Galerkin method for operator-differential equations, Diff. Equations, V.22 (1986), pp.2135–2144.MathSciNetGoogle Scholar
  3. [3]
    S.G. Mikhlin, Variational Methods in Mathematical Physics, Moscow, Nauka (1970).Google Scholar
  4. [4]
    P.E. Sobolevskiy, On equations with operators, forming acute angle, Dokl. AN SSSR, V.116 (1957), pp.754–757.Google Scholar
  5. [5]
    A.G. Zarubin, On iterative method of solving Cauchy problem for quasi-linear differential-operator equation, Izvestiya Vuzov, Mathematics, V.12 (1992).Google Scholar
  6. [6]
    V.B. Demidovich, On asymptotic behavior of solutions of finite-difference equations. 1. General aspects, Diff. Equations, V.10 (1974), pp.2267–2278.Google Scholar
  7. [7]
    A.G. Zarubin, On a convergance rate of Faedo-Galerkin method for quasi-linear non-stationary operator equations, Diff.Equations, V.26 (1990), pp.2051–2059.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • A. G. Zarubin
    • 1
  1. 1.State University of TechnologyKhabarovskRussia

Personalised recommendations