A pseudospectral method for budget-constrained infinite horizon optimal control problems

In this paper a generalization of the indirect pseudo-spectral method, presented in [17], for the numerical solution of budget-constrained infinite horizon optimal control problems is presented. Consideration of the problem statement in the framework of weighted functional spaces allows to arrive at a good approximation for the initial value of the adjoint variable, which is inevitable for obtaining good numerical solutions. The presented method is illustrated by applying it to the budget-constrained linear-quadratic regulator model. The quality of approximate solutions is demonstrated by an example.

Regularized Collocation in Distribution of Diffusion Times Applied to Electrochemical Impedance Spectroscopy

This paper is inspired by recently proposed approach for interpreting data of Electrochemical Impedance Spectroscopy (EIS) in terms of Distribution of Diffusion Times (DDT). Such an interpretation requires to solve a Fredholm integral equation of the first kind, which may have a non-square-integrable kernel. We consider a class of equations with above-mentioned peculiarity and propose to regularize them in weighted functional spaces. One more issue associated with DDT-problem is that EIS data are available only for a finite number of frequencies. Therefore, a regularization should unavoidably be combined with a collocation. In this paper we analyze a regularized collocation in weighted spaces and propose a scheme for its numerical implementation. The performance of the proposed scheme is illustrated by numerical experiments with synthetic data mimicking EIS measurements.

Some nonlocal problems for second order strictly hyperbolic systems on the plane

Some nonlocal problems for one class of second order strictly hyperbolic systems in a strip on the plane are considered in weighted functional spaces. Proceeding from the structure of solutions of hyperbolic systems and using the methods of complex analysis conditions are found for weight exponents of functional spaces which ensure well-posedness of considered problems.

On Some Boundary Value Problems for an Ultrahyperbolic Equation

The correct formulation of a characteristic problem and a Darboux type problem in the special weighted functional spaces for an ultrahyperbolic equation is investigated.