Georgian Mathematical Journal 13 (2006), No. 2, 343--362
Copyright Heldermann Verlag 2006
An Automatically Stable and Order Three Split Rational Approximation of a Semigroup
Jemal Rogava
I. Vekua Inst. of Applied Mathematics, I. Javakhishvili State University, 2 University Street, Tbilisi 0143, Georgia
jrogava@viam.hepi.edu.ge
Mikheil Tsiklauri
I. Vekua Inst. of Applied Mathematics, I. Javakhishvili State University, 2 University Street, Tbilisi 0143, Georgia
mtsikla@viam.hepi.edu.ge
[Abstract-pdf]
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: 65M12, 65M15, 65M55
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