Department of Mathematics
The existence and uniqueness of solutions and convergence of
iterative methods for general differential-algebraic systems
Zbigniew Bartoszewski
Gdansk University of Technology
The talk will be devoted to quite general classes of integro-algebraic and differential-algebraic systems. We do not require from the operators involved in the definitions of the systems under consideration to be of Voltera type. The existence and uniqueness of solutions to such systems as well as the convergence of different iterative processes of their solution including waveform relaxation methods will be discussed. There will be given constructive sufficient conditions under which the solutions exist and the iterative processes are convergent. A special attention will be paid to quasi-linear systems of differential-algebraic equations. A number of different iterative processes for their solution will be considered. The relationship between the spectral radii of the matrices that define the corresponding majorizing iterative processes will be provided. The talk will be concluded with numerical examples which illustrate how these spectral radii influence the rate of convergence of the iterative processes.
All interested persons are welcome.
The talk will be accessible to upper class students.