Mayko N.V.
Super-exponential rate of convergence of the Cayley transform method for an abstract differential equation

A boundary-value problem (BVP) for a second-order abstract differential equation with an operator coefficient in a Hilbert space is investigated. The exact solution is presented as an infinite series by means of the Cayley transform of the operator coefficient A and the polynomials of Meixner type in the independent variable x. The approximate solution is given by the truncated sum of the series with N addends. The error estimates (with the weighted function) depending not only on the discretization parameter N but also on the distance of the argument x to the boundary points of the segment are proved. The algorithm has a super-exponential rate of convergence. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: boundary-value problem (BVP), Cayley transform, Hilbert space, operator coefficient, super-exponentially convergent algorithm, weighted estimates, Approximation theory, Boundary value problems, Polynomials, Abstract differential equations, Approximate solution, Cayley transforms, Discretization parameters, Error estimates, Independent variables, Super-exponential, Weighted function, Graph Databases

Cite:
Mayko N.V. (2020). Super-exponential rate of convergence of the Cayley transform method for an abstract differential equation. Cybernetics and Systems Analysis, 56 (3), 171–183. doi: https://doi.org/10.1007/s10559-020-00265-2 http://jnas.nbuv.gov.ua/article/UJRN-0001121529 [In Ukrainian].