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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Gauss-Type Quadratures For Weakly Singular Integrals And Their Application To Fredholm Integral Equations Of The Second Kind, Hideaki Kaneko, Yuesheng Xu
Gauss-Type Quadratures For Weakly Singular Integrals And Their Application To Fredholm Integral Equations Of The Second Kind, Hideaki Kaneko, Yuesheng Xu
Mathematics & Statistics Faculty Publications
In this paper we establish Gauss-type quadrature formulas for weakly singular integrals. An application of the quadrature scheme is given to obtain numerical solutions of the weakly singular Fredholm integral equation of the second kind. We call this method a discrete product-integration method since the weights involved in the standard product-integration method are computed numerically.
Periodic And Homoclinic Orbits In A Toy Climate Model, M. Toner, A. D. Kirwan Jr.
Periodic And Homoclinic Orbits In A Toy Climate Model, M. Toner, A. D. Kirwan Jr.
Mathematics & Statistics Faculty Publications
A two dimensional system of autonomous nonlinear ordinary differential equations models glacier growth and temperature changes on an idealized planet. We apply standard perturbative techniques from dynamical systems theory to study small amplitude periodic orbits about a constant equilibrium. The equations are put in cononical form and the local phase space topology is examined. Maximum and minimum periods of oscillation are obtained and related to the radius of the orbit. An adjacent equilibrium is shown to have saddle character and the inflowing and outflowing manifolds of this saddle are studied using numerical integration. The inflowing manifolds show the region of …
A Fast Numerical Solution Of Scattering By A Cylinder: Spectral Method For The Boundary Integral Equations, Fang Q. Hu
A Fast Numerical Solution Of Scattering By A Cylinder: Spectral Method For The Boundary Integral Equations, Fang Q. Hu
Mathematics & Statistics Faculty Publications
It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converge slowly for high frequency waves. In this paper, a fast numerical solution is presented for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of …
Continuity Of Metric Projection, Pólya Algorithm, Strict Best Approximation, And Tubularity Of Convex Sets, Robert Huotari, Wu Li
Continuity Of Metric Projection, Pólya Algorithm, Strict Best Approximation, And Tubularity Of Convex Sets, Robert Huotari, Wu Li
Mathematics & Statistics Faculty Publications
The notion of tubularity of a convex subset, K, of l∞ (n) was originally introduced to study the convergence of the Pólya algorithm. It is shown in the present paper that this geometric condition provides a characterization of thosed closed convex sets onto which the set-valued metric projection is continuous. In the development of this result, Rice′s strict best approximation is characterized in three new ways, and is shown, assuming tubularity of K, to be a continuous selection. The class of sets on which the Pólya algorithm is known to converge is enlarged to include …
Some Triple Sine Series, G. Kerr, G. Melrose, J. Tweed
Some Triple Sine Series, G. Kerr, G. Melrose, J. Tweed
Mathematics & Statistics Faculty Publications
Two types of triple sine series are investigated. They are reduced to singular integral equations with kernels involving elliptic functions. Closed form solutions are obtained.