Geodesic
Error estimates for projection-difference methods for differential equations with differentiable operators
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2010), pp. 3-15

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We study the projection-difference methods for approximate solving the Cauchy problem for operator-differential equations with a leading self-adjoint operator $A(t)$ and a subordinate linear operator $K(t)$, whose definition domain is independent of $t$. Operators $A(t)$ and $K(t)$ are assumed to be sufficiently smooth. We obtain estimates for the rate of convergence of approximate solutions to the exact solution as well as those for fractional degrees of an operator similar to $A(0)$.
Keywords: Hilbert space, Cauchy problem, Galyorkin method, three-level scheme, operator equation, orthoprojector
Mots-clés : convergence rate. 
@article{IVM_2010_7_a0,
     author = {P. V. Vinogradova},
     title = {Error estimates for projection-difference methods for differential equations with differentiable operators},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--15},
     publisher = {mathdoc},
     number = {7},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_7_a0/}
}
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P. V. Vinogradova. Error estimates for projection-difference methods for differential equations with differentiable operators. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2010), pp. 3-15. http://geodesic.mathdoc.fr/item/IVM_2010_7_a0/