Numerical methods for solving the control problems for processes described by differential and integro-differential equations

Project type: Gant funding for the Science Committee Ministry of Education and Science of the RK

Code of the project: AP05132455 (01.01.2018 – 31.12.2020)

Title: Numerical methods for solving the control problems for processes described by differential and integro-differential equations.

The object of research, development or design: Boundary value problems for the differential, loaded differential and integro-differential equations;

Approximate and numerical methods for solving the boundary value problems for the differential and integro-differential equations.

Aim of work: Develop effective numerical methods for solving the control problems of processes described by differential and integro-differential equations:

–  construct numerical algorithms of parameterization method for solving the control problems for ordinary differential and integro-differential equations with parameters;

–  construct numerical algorithms of parameterization method for solving the control problems for differential and integro-differential equations in partial derivatives;

–  establish the solvability conditions for the investigated problems and the convergence of the proposed algorithms.

Research methods: To achieve the Project goal, the control problems for differential and integro-differential equations with parameters, the control problems for differential and integro-differential equations in partial derivatives are investigated by the parameterization method.

Field of application: Currently, the problem of constructing effective models finds its solution in many areas of science and technology. The active development of computer technology in recent decades, the emergence of new software tools designed to automate professional activity, has significantly affected the methods for solving the problems of identification of parameters. The application of software tools specialized in the field of scientific, technical and engineering calculations provides an opportunity for a deeper study of the investigated area, transferring the main burden of solving the problems from the development, debugging of algorithms and programs to the study of qualitative and numerical characteristics of the problem. Therefore, a modern approach in the theory of control and identification of parameters should be directed to the development of new constructive methods and modifications of known methods for solving the process control problems described by differential and integro-differential equations. These classes of problems arise in the mathematical modeling of phenomena and processes in biology, chemistry, physics, economics, etc. [1-15].

Project Investigator: Bakirova E.A. (IICT CS MES RK)

The organization – executor: IICT CS MES RK