Integral equations on compact manifold with boundary

Solving coupled Dyson–Schwinger equations on a compact manifold

A generic numerical method to solve a coupled set of Dyson–Schwinger equations on a compact manifold is presented. It is exemplified employing a truncated, closed set of equations for the gluon and ghost propagators in SU(N) Yang–Mills theory on a four-torus at zero and nonzero temperatures. When compared to continuum solutions at zero temperature sizeable modifications due to the finite volume...

Controllability of two coupled wave equations on a compact manifold

We consider the exact controllability problem on a compact manifold Ω for two coupled wave equations, with a control function acting on one of them only. Action on the second wave equation is obtained through a coupling term. First, when the two waves propagate with the same speed, we introduce the time Tω→O→ω for which all geodesics traveling in Ω go through the control region ω, then through ...

CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

Struwe’s decomposition for a Polyharmonic operator on a compact Riemannian manifold with or without boundary

The Numerical Solution of Boundary Integral Equations

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...