Український математичний конгрес  2009
Віталій Василик (Інститут математики НАН України, Київ, Україна) Exponentially convergent method for mpoint nonlocal problem for the first order differential equation in Banach space The mpoint 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 DunfordCauchy integral along a hyperbola enveloping the spectrum of A and on the proper quadratures involving short sums of resolvents. The efficiency of the proposed algorithm is demonstrated by numerical examples.
