Exponentially convergent algorithm for a second order differential equation with an operator coefficient in Banach space

by    I. P. Gavriljuk, V. L. Makarov, V. Vasylyk

Preprint series: 06-27, Reports on Numerical Mathematics

I. P. Gavriljuk, V. L. Makarov, V. Vasylyk

Preprint series: , Reports on Numerical Mathematics

MSC:
65J10 Equations with linear operators (do not use 65Fxx)
65M12 Stability and convergence of numerical methods
65M15 Error bounds
65M06 Finite difference methods
65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
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: We propose and justify an exponentially convergent algorithm for
a second order differential equation with an operator coefficient in
Banach space. A particular example of such equation is the strongly
damped wave equation arising in viscoelasticity.
Numerical examples are given which confirm theoretical results.

Keywords: Second order differential equation with an operator coefficient in Banach space, strongly damped wave equation, operator exponential, Sinc-quadratures, exponentially convergent algorithms

Upload: 2006-12-22

Update: 2006


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