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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.
In the present work the symmetrized sequential-parallel decomposition method
of the third degree precision for the solution of Cauchy abstract problem
with an operator under a split form, is presented. The third degree
precision is reached by introducing a complex coefficient with the positive
real part. For the considered schema the explicit a priori estimation is
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