arXiv subjects

V. B. Vasylyk

Publications and source records attributed to V. B. Vasylyk.

2 recordsLinked to original sources

arXiv2013

Exponentially convergent method for integral nonlocal problem for the first order differential equation with unbounded coefficient in Banach space

Problem for the first order differential equation with an unbounded operator coefficient in Banach space and integral nonlocal condition is considered. An exponentially convergent algorithm is proposed and justified for the numerical solution of this problem in assumption that an operator coefficient $A$ is strongly positive and some existence and uniqueness conditions are fulfilled. This algorithm is based on the 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 several numerical examples.

math.NA↗

arXiv2010

Two-points problem for an evolutional first order equation in Banach space

Two-points nonlocal problem for the first order differential evolution equation with an operator coefficient 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 uniqueness 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.

math.NA↗