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A new exponentially convergent algorithm is proposed for an abstract thefirst order differential equation with unbounded operator coefficientpossessing a variable domain. The algorithm is based on a generalization of theDuhamel integral for vector-valued functions. This technique translates theinitial problem to a system of integral equations. Then the system isapproximated with exponential accuracy. The theoretical results are illustratedby examples associated with the heat transfer boundary value problems.

Approximate solution to abstract differential equations with variable domain