Weighted Estimates of the Cayley Transform Method for Abstract Differential Equations-Reference-Cited by-同舟云学术

Weighted Estimates of the Cayley Transform Method for Abstract Differential Equations

Published:2020-02-07 Issue:1 Volume:21 Page:53-68
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Gavrilyuk Ivan P.¹^ORCID,Makarov Volodymyr L.²^ORCID,Mayko Nataliya V.³^ORCID

Affiliation:

1. University of Cooperative Education Gera-Eisenach , Am Wartenberg 2, 99817 Eisenach , Germany

2. Department of Numerical Mathematics , Institute of Mathematics of the National Academy of Sciences of Ukraine , 3 Tereshchenkivska Str., 01024 Kyiv , Ukraine

3. Department of Mathematics and Theoretical Radiophysics , Taras Shevchenko National University of Kyiv , 64/13 Volodymyrska Str., 01601 Kyiv , Ukraine

Abstract

Abstract We represent the solution u ⁢ ( t )

{u(t)}

of an initial value problem (IVP) for the first-order differential equation with an operator coefficient as a series using the Cayley transform of the corresponding operator coefficient and the Laguerre polynomials. In the case of a boundary value problem (BVP) for the second-order differential equation with an operator coefficient, we represent its solution using the Cayley transform and the Meixner-type polynomials. The approximate solution is the truncated sum of N (the discretization parameter) summands. We give the error estimate of these approximations depending on N and the distance of t to the initial point of the time interval or of the spatial argument x to the boundary of the spatial domain.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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