Date of Online Publication: 02/11/2010 Keywords: Edge detection, discontinuities, wavelets, polyharmonic splines.
Abstract: In this paper we consider the problem of detecting, from a finite discrete set of points, the curves across which a two-dimensional function is discontinuous. We propose a strategy based on wavelets which allows to discriminate the edge points from points in which the function has steep gradients or extrema.
Date of Online Publication: 02/11/2010 Keywords: Partial Differential Equations, Meshless Method, Radial Basis Function, Radial Point Interpolation
Abstract: A meshless method based on radial point interpolation was recently developed as an effective tool for solving partial differential equations, and has been widely applied to a number of different problems. In addition to the primary advantage of the meshless methods that the computation is performed without any connectivity information between field nodes, the radial point interpolation-based meshless method has several advantages such as the stability of the shape functions and simple implementation of boundary condition enforcement. This paper introduces a new scheme for the radial point interpolation-based meshless method. This method enables fast computation by modifying the construction and evaluation of the shape functions. Numerical examples are also presented to show that a reliable solution can be obtained with low computational cost.
Date of Online Publication: 02/11/2010 Keywords: Existence results, beam vibration, damping, hybrid model.
Abstract: We consider the solvability of a hybrid model for the vibration of a vertical slender structure mounted on an elastic seating. The slender structure is modeled as a Rayleigh beam and gravity is taken into account. The seating and foundation block are modeled as rigid bodies connected by elastic springs with damping mechanisms. We show how an existence result for a general linear vibration problem in variational form may be applied to the weak variational problem for this system.
Date of Online Publication: 02/11/2010 Keywords: Stochastic Differential Equations, Additive Noise, Numerical Solution, Runge– Kutta methods Periodic orbits, Numerical drift. Authors: Foivos Xanthos and George Papageorgiou
Abstract: In this paper we study the numerical treatment of Stochastic Differential Equations with additive noise and one dimensional Wiener process. We develop two, three and four stage Runge–Kutta methods which attain deterministic order up to four and stochastic order up to one and a half specially constructed for this class of problems. Numerical tests and comparisons with other known methods in the solution of various problems justify our effort, especially for our three stages methods.
Date of Online Publication: 02/11/2010 Keywords: Time reversal symmetry, Reversible Hamiltonian systems, Symmetric methods, Periodic orbits, Numerical drift. Authors: Pages:
Abstract: When approximating reversible Hamiltonian problems, the presence of a “drift” in the numerical values of the Hamiltonian is sometimes experienced, even when reversible methods of integration are used. In this paper we analyze the phenomenon by using a more precise definition of time reversal symmetry for both the continuous and the discrete problems. A few examples are also presented to support the analysis.