We present greedy unsymmetric collocation schemes for solving linear elliptic partial differential equations using radial basis functions. The proposed approach circumvents the ill-conditioning problem associated with the standard collocation technique and enables the efficient solution of problems requiring a large set of collocation points. Numerical studies indicate that the accuracy of gree...

Keywords: Volterra integro-differential equations Multistep collocation Superconvergence Stability a b s t r a c t Multistep collocation methods for Volterra integro-differential equations are derived and analyzed. They increase the order of convergence of classical one-step collocation methods, at the same computational cost. The numerical stability analysis is carried out and classes of A 0-s...

In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of “blow-up collocation solution” and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we d...

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...

We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples ...

‎the main purpose of this paper is to study the numerical solution of nonlinear volterra integral equations with constant delays, based on the multistep collocation method. these methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. also, we analyze the convergence of the...

Noise from the auxiliary power unit (APU) is becoming an increasingly important aircraft design constraint because of the noise exposure during ground operations (“ramp-noise”). Reduction of noise may be achieved by liners in the exhaust duct. In this paper, we will consider the propagation of sound through the APU exhaust duct, which is typically straight with an axially varying liner depth, a...

The goal of control law design for haptic displays is to provide a safe and stable user interface while maximizing the operator’s sense of kinesthetic immersion in a virtual environment. This paper outlines a control design approach which stabilizes a haptic interface when coupled to a broad class of human operators and virtual environments. Two-port absolute stability criteria are used to deve...