Matviy O. Investigation of approximation schemes of functional differential equations

In the thesis the accuracy of approximation of concatenated vector elements with delay depending on the smoothness of the input function is established. The scheme of the approximation of initial problems is constructed and proved for systems of differential-difference equations of the delayed and neutral types and linear functional differential equations. Conditions of the solvability of boundary value problems with delay are proved and their approximation is investigated with the help of systems of ordinary differential equations. Algorithms of approximated finding of non-asymptotic roots of quasi-polynomials for systems of linear differential-difference equations with many delays are constructed and proved with the help of above mentioned approximation schemes. Algorithms of the investigation of the stability of linear autonomous systems with delay are analyzed.