**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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