**Jemal Rogava, Mikheil Tsiklauri**

## An Automatically Stable and
Order Three Split Rational Approximation of a Semigroup

**Abstract:**

An automatically stable and order three split rational approximation scheme is
proposed for solving the Cauchy abstract problem. The third order precision is
obtained by introducing the complex parameter $\alpha =\frac{1}{2}\pm i\frac{1}{2\sqrt{3}}$
and performing a rational approximation of the semigroup. For the considered
scheme, an explicit a priori estimate is derived.

**Keywords:**

Decomposition method, operator split, semigroup, Trotter formula, Cauchy
abstract problem, rational approximation.

**MSC 2000:** 65M12, 65M15, 65M55