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