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|Title:||Two-points problem for an evolutional ﬁrst order equation in Banach space|
|Keywords:||First order diﬀerential evolution equations in Banach space, nonlocal problem, unbounded operator coeﬃcient, operator exponential, exponentially convergent algorithms|
|Abstract:||Two-point nonlocal problem for the ﬁrst order diﬀerential evolution equation with an operator co- eﬃcient in a Banach space X is considered. An exponentially convergent algorithm is proposed and justiﬁed in assumption that the operator coeﬃcient is strongly positive and some existence and unique- ness conditions are fulﬁlled. This algorithm leads to a system of linear equations that can be solved by ﬁxed-point iteration. The algorithm provides exponentially convergence in time that in combination with fast algorithms on spatial variables can be eﬃcient treating such problems. The eﬃciency of the proposed algorithms is demonstrated by numerical examples.|
|Appears in Collections:||Наукові роботи співробітників кафедри прикладної математики|
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