Exponentially convergent Duhamel´s like algorithms for differential equations with an operator coefficient possessing a variable domain in Banach space

by    T. Ju. Bohonova, I. P. Gavrilyuk, V. L. Makarov, V. Vasylyk

Preprint series: 05-06, Reports on Numerical Mathematics

Preprint series: , Reports on Numerical Mathematics

65J10 Equations with linear operators (do not use 65Fxx)
65M12 Stability and convergence of numerical methods
65M15 Error bounds
46N20 Applications to differential and integral equations
46N40 Applications in numerical analysis [See also 65Jxx]
47N20 Applications to differential and integral equations
47N40 Applications in numerical analysis [See also 65Jxx]

Abstract: 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 the Duhamel´s integral for vector-valued functions which allows to translate the initial problem into a boundary integral equation and then approximate it with exponential accuracy. Examples of boundary value problems for the heat equation with time-dependent boundary conditions are given which confirm and illustrate the theoretical results obtained.

Keywords: First order differential equations in Banach space, operator coefficient with a variable domain, Duhamel´s integral, operator exponential, exponentially convergent algorithms

Upload: 2005-06-27

Update: 2005

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