Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in moder power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. These integral equations efficiently solve such inverse problem taking into a...

Much of the research on the numerical analysis of Fredholm type integral equations during the past ten years has centered on the solution of boundary integral equations (BIE). A great deal of this research has been on the numerical solution of BIE on simple closed boundary curves S for planar regions. When a BIE is de ned on a smooth curve S, there are many numerical methods for solving the equ...

A long-standing open question associated with the use of collocation methods for boundary value ordinary differential equations is concerned with the development of a high order continuous solution approximation to augment the high order discrete solution approximation, obtained at the mesh points which subdivide the problem interval. It is well known that the use of collocation at Gauss points...

Two piecewise Hermite bicubic orthogonal spline collocation schemes are considered for the approximate solution of elliptic, self-adjoint, nonhomogeneous Dirichlet boundary value problems on rectangles. In the rst scheme, the nonhomogeneous Dirichlet boundary condition is approximated by means of the piecewise Hermite cubic interpolant, while the piecewise cubic interpolant at the boundary Gaus...

Abstract. A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian satisfies a strong convexity condition, then the discrete problem possesses a local minimizer in a neighborhood of the continuous solution, and as the...

Second-kind Volterra integral equations with weakly singular kernels typically have solutions which are nonsmooth near the initial point of the interval of integration. Using an adaptation of the analysis originally developed for nonlinear weakly singular Fredholm integral equations, we present a complete discussion of the optimal (global and local) order of convergence of piecewise polynomial ...

We compare piecewise linear and polynomial collocation approaches for the numerical solution of a Fredholm integro-differential equations modelling neural networks. Both approaches combine the use of Gaussian quadrature rules on an infinite interval of integration with interpolation to a uniformly distributed grid on a bounded interval. These methods are illustrated by numerical experiments on ...

In this paper we investigate collocation methods for the computation of periodic solutions of autonomous delay diierential equations (DDEs). Periodic solutions are found by solving a periodic two-point boundary value problem, which is an innnite-dimensional problem for DDEs, in contrast to the case of ordinary diierential equations. We investigate three collocation methods based on piecewise po...