Asymptotic error estimates of a~linearized projection-difference method for a~differential equation with a~monotone operator

P. V. Vinogradova ; A. G. Zarubin

Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 387-401.

Résumé

In this paper, we study a projection-difference method for the Cauchy problem for an operator-differential equation with a self-adjoint leading operator $A(t)$ and a non-linear monotone subordinate operator $K(\cdot)$ in a Hilbert space. This method leads to solving a system of linear algebraic equations at each time level. Error estimates for the approximate solutions as well as for the fractional powers of the operator $A(t)$ are obtained. The method is applied to a model parabolic problem.

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