In the present work, the symmetrized sequential-parallel decomposition method with the fourth order accuracy for the solution of Cauchy abstract problem with an operator under a split form is presented. The fourth order accuracy is reached by introducing a complex coefficient with the positive real part. For the considered scheme, the explicit a priori estimate is obtained.

Classification: 65M12, 65M15, 65M55

Keywords: decomposition method, semigroup, operator split method, Trotter formula, Cauchy abstract problem

@article{M2AN_2004__38_4_707_0, author = {Gegechkori, Zurab and Rogava, Jemal and Tsiklauri, Mikheil}, title = {The fourth order accuracy decomposition scheme for an evolution problem}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, publisher = {EDP-Sciences}, volume = {38}, number = {4}, year = {2004}, pages = {707-722}, doi = {10.1051/m2an:2004031}, zbl = {1077.65101}, mrnumber = {2087731}, language = {en}, url = {http://www.numdam.org/item/M2AN_2004__38_4_707_0} }

Gegechkori, Zurab; Rogava, Jemal; Tsiklauri, Mikheil. The fourth order accuracy decomposition scheme for an evolution problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 4, pp. 707-722. doi : 10.1051/m2an:2004031. http://www.numdam.org/item/M2AN_2004__38_4_707_0/

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