Publication Info
- Title:
- Exponentially Convergent Method for the m-Point Nonlocal Problem for a First Order Differential Equation in Banach Space
- Type:
- Article
- Status:
- Published
- Journal:
- Numerical Functional Analysis and Optimization 31, no. 1 (February 2010): 1–21
Abstract
The m-point nonlocal problem for the first-order differential equation with an operator coefficient in a Banach space X is considered. An exponentially convergent algorithm is proposed and justified provided that the operator coefficient A is strongly positive and some existence and uniqueness conditions are fulfilled. This algorithm is based on representations of operator functions by a Dunford–Cauchy integral along a hyperbola enveloping the spectrum of A and on the proper quadratures involving short sums of resolvents. The efficiency of the proposed algorithms is demonstrated by numerical examples.