Projection Method for Cauchy Problem for an Operator-Differential Equation |
| |
| Authors: | Polina Vinogradova Anatoli Zarubin |
| |
| Institution: | 1. Department of Natural Sciences , Far Eastern State Transport University , Khabarovsk, Serisheva, Russia vpolina17@hotmail.com;3. Department of Natural Sciences , Far Eastern State Transport University , Khabarovsk, Serisheva, Russia |
| |
| Abstract: | In the current paper, we study a projection method for a Cauchy problem for an operator-differential equation with a leading self-adjoint operator A(t) and a subordinate linear operator K(t) in a Hilbert space. The projection subspaces are linear spans of eigenvectors of an operator similar to A(t). It is assumed that the operators A(t) and K(t) are sufficiently smooth. Error estimates for the approximate solutions and their derivatives are obtained. The application of the developed method for solving the initial boundary value problems is given. |
| |
| Keywords: | Cauchy problem Galerkin method Hilbert space Operator equation Orthogonal projection |
|
|
