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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… (More)

- T. Yu. Bohonova, Ivan P. Gavrilyuk, Volodymyr L. Makarov, V. Vasylyk
- SIAM J. Numerical Analysis
- 2007

A suitable abstract setting of the initial value problem for the first order differential equation with an unbounded operator coefficient in a Banach space where the domain of the operator depends on the dependent variable t is introduced. A new exponentially convergent algorithm for such problems is proposed. This algorithm is based on a generalization of… (More)

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