**7. Conclusions**

This paper dealt with a new approach to the algorithm of the method of boundary functions from [4] for asymptotic solving initial value problem of form (1)-(2) in the critical case. Namely, the algorithm was formulated with the help of orthogonal projectors of the space *X* onto *kerA*(*t*) and *kerA*(*t*) . Such an approach clearly shows the structure of the algorithm for finding asymptotics terms, given in Tables 1 and 2 of the paper.

**Funding:** This research was funded by the RUSSIAN SCIENCE FOUNDATION, grant number 17-11-01220.

**Acknowledgments:** The author thank the anonymous referees for carefully reading the paper and for the numerous critical and constructive comments that have helped to improve the paper text. She thanks also N. T. Hoai for useful discussions and M. A. Kalashnikova for the help in printing the paper text.

**Conflicts of Interest:** The author declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

### **References**


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