Publication Info
- Title:
- Exponentially convergent numerical method for the first order differential equation in Banach space and two-point nonlocal condition with unbounded operator (In Ukrainian)
- Type:
- Article
- Status:
- Published
- Journal:
- Collected works of Institute of mathematics of National Academy of Sciences, 2015, v. 12 (5)
Abstract
Problem for the first order differential equation with an unbounded operator coefficient in Banach space and two-pointed nonlocal condition is considered. It is assumed that the nonlocal condition possesses an unbounded operator coefficient. An exponentially convergent algorithm is proposed and justified for the numerical solution of this problem under assumption that the operator coefficient $A$ is sectorial and some existence and uniqueness conditions are fulfilled. The proposed algorithm is based on the application of Sinc-quadrature formulae to the Dunford-Cauchy integral representation of the solution operator and, as a result, requires only a small number of resolvent evaluations.The efficiency of the proposed algorithm is demonstrated by several numerical examples.