Jemal Rogava, Mikheil Tsiklauri

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

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.

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

MSC 2000: 65M12, 65M15, 65M55