Project's information

Project's title Numerical methods and investigation of integral differential equations with identically degenerate leading parts and singularities
Project’s code QTRU01.08/20-21
Research hosting institution Institute of Mathematics
Coordinating unit, co-chair Basic National Foudnation, Russian
Project leader’s name Asscoc. Prof. Doan Thai Son and Dr. Liubov S. Solovarova
Project duration 01/06/2020 - 30/06/2022
Project’s budget 200 million VND
Classify Fair
Goal and objectives of the project

In a continuation of the existing research coopearation on differential equations and control theory between scientific members of Institute of Mathematics, VAST and Institute of Systems Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences, the aim of the project is to make a cooperation in finding a new and feasible method in solving differential-integral equations with singular coefficiences. Based on the cooperation,  the outcome of the project might enhance the research and applications of ODE and DAE in Vietnam. Some new research results might be taught at Vietnam.

Main results

Research achievement: The members have constructed a suitable space for the solutions and then have proved the well-posedness of solutions for Caputo stochastic differential equations. On the other side, the members have also constructed a suitable state linear feedback for the problem in assigning spectrum of time-varying linear control systems.
In the cooperation aspect, the members of two gropuh have discussed and completed some new numerical schemes with their stability properties for  differential-integral equations with singular coefficiences.
Education and training: The project partially supported 02 Phd students, one of them defended successfully the thesis and received PhD degree. 

Novelty and actuality and scientific meaningfulness of the results

- Establishing a new result about regularity of solutions for stochastic differential equatins with singular coefficiences. 
- Estabalishing a new result on necessary and sufficient conditions for assignment of spectrum of limear time-varying control systems
-  Developing some new results on the numerical solutions of algebraic differential equations.

Products of the project

- Publications:
1. Artur Babiarz, Le Viet Cuong, Adam Czornik, Đoàn Thái Sơn, Necessary and sufficient conditions for assignability of dichotomy spectrum of one-sided discrete time-varying linear systems, IEEE-Transactions on Automatic Control, Volume 67 (2022), Issue 4, 2039-2043. (SCI-E)
2. Phan Thi Huong, Peter Kloeden, Đoàn Thái Sơn, Well-posedness and regularity for solutions of Caputo stochastic fractional differential equations in $ L^p $ spaces. To appear in Stochastic Analysis and Application. DOI: 10.1080/07362994.2021.1988856. (SCI-E)
3. E. V. Chistyakova, L. S. Solovarova, Doan Thai Son, A numerical method for solving singular integral algebraic equations with weakly singular kernels, Vestn. YuUrGU. Ser. Vych. Matem. Inform., 2021, Volume 10, Issue 3, 5–15. DOI:
4. L. S. Solovarova, T. D. Phuong. On the numerical solution of second-order stiff linear differential-algebraic equations. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. :(2021), 1–10. DOI:–10.
- Other products: 02 Phd students have been partially supported.


Continue supporting the research cooperation on differential equations and control theory between two units: of Institute of Mathematics, VAST and Institute of Systems Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences