UDC 519.6
1 Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
 makarovimath@gmail.com
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2 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
mayko@knu.ua
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UNIMPROVABLE ERROR ESTIMATES OF THE CAYLEY TRANSFORM METHOD
FOR THE OPERATOR EXPONENTIAL FUNCTION IN A HILBERT SPACE
Abstract. We obtain the error estimate of the Cayley transform method for solving the abstract Cauchy problem for the first-order
differential equation with an unbounded operator coefficient in a Hilbert space.
The estimate indicates that our method has a power rate of convergence which automatically depends
on the smoothness of the initial data (i.e., our method is a method without saturation of accuracy).
Moreover, we substantiate that the estimate is unimprovable in the order
of N (the discretization parameter N characterizes the number of summands in the partial sum for the approximate solution).
Keywords: differential equation, Cauchy problem, operator exponential function, Hilbert space, Cayley transformation, error estimate.
full text
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